Sampling method considering space-time mode heterogeneity, medium and equipment

Abstract

The invention relates to a sampling method considering space-time mode heterogeneity, a medium and equipment. The method comprises the following steps: performing spatio-temporal pattern recognition on a spatio-temporal data set based on dynamic pattern decomposition, extracting spatio-temporal variation characteristic parameters in a research area, and dividing the research area into a plurality of geographic subunits with spatio-temporal variation pattern heterogeneity characteristics; generating candidate points in the geographic subunits by adopting a grid generation technology, and selecting part of the candidate points as an initial sampling point set; matching an independent space-time prediction model for each geographic subunit, performing space-time prediction on non-sampling points by using the sampling points in the subunits, and calculating space-time prediction errors of the non-sampling points in the subunits; on the basis of an error feedback mechanism, according to the space-time prediction error and the preset sampling frequency and number, the position of a newly-added sampling point is judged, and the sampling point set in the subunit is updated; and performing loop iteration until a sampling stop condition is met. According to the invention, the sampling problem under the heterogeneous spatio-temporal mode in a complex geographical environment is effectively solved.

Description

Technical Field

[0001] The present invention relates to the technical field of geographic statistical spatial data sampling, and in particular to a sampling method, medium and equipment that take into account the heterogeneity of temporal and spatial patterns. Background Art

[0002] Spatial statistical sampling is a key link in data collection and analysis. By scientifically designing sampling strategies, comprehensive, accurate and representative data can be obtained under limited resource conditions, providing a solid foundation for subsequent spatial analysis, modeling and prediction. In traditional research, many sampling methods usually assume that the target observations are regularly distributed in the spatial and temporal dimensions, that is, it is assumed that the target variables have a consistent spatiotemporal variation pattern in the study area. For example, the sampling model proposed by Lv et al. in "Towards sustainability: The spatiotemporal patterns and influence mechanismof urban sprawl intensity in the Yangtze River Delta urban agglomeration" and the sampling model proposed by Madhwal et al. in "Evaluation of PM 2.5 The sampling strategy proposed in "Spatio-temporal variability and hotspot formation using low-cost sensors across urban-rural landscape in Lucknow" and the model proposed by Niu et al. in "Spatiotemporal patterns and drivers of the urban air pollution island effect for 2273 cities in China" both assume that the spatial and temporal distribution trends of environmental variables are consistent within a region. However, this assumption simplifies model design while ignoring the temporal and spatial heterogeneity that is prevalent in real-world scenarios, potentially impacting sampling quality and accuracy.

[0003] A spatio-temporal pattern refers to the distribution law and changing trend of a target variable in the spatial and temporal dimensions. It not only reflects the distribution characteristics of the variable at different spatial positions but also reveals the regularity of the variable's dynamic changes over time. Specifically, spatio-temporal patterns can describe the spatial distribution gradient, temporal change trend, and the interaction between space and time of the variable within a region. For example, the air pollution concentration in urban areas may show a temporal pattern of being higher during the day and lower at night, and at the same time, it shows a distribution characteristic of higher pollution concentration in industrial areas and lower pollution concentration in green spaces in terms of space. However, spatio-temporal pattern heterogeneity is prevalent in complex geographical environments. Spatio-temporal pattern heterogeneity refers to the significant differences shown by the target variable between different spatial units and over the temporal dimension. It includes: the target variable presenting significantly different distribution characteristics between different spatial regions, the dynamic change law of the target variable varying due to regional characteristics over the temporal dimension, and the combined effect of spatial heterogeneity and temporal heterogeneity resulting in a more complex change pattern of the target variable in the spatio-temporal dimension.

[0004] Traditional sampling methods usually assume that the target variable has a single spatio-temporal change pattern within the study area, that is, it is considered that the variable change trend is consistent throughout the area. However, this assumption ignores the actual multi-spatio-temporal pattern characteristics within the area. Multi-spatio-temporal patterns refer to the existence of multiple independent or interacting spatio-temporal change patterns within a region, and these patterns may be jointly determined by geographical features (such as terrain, land use type), socio-economic factors (such as industrial distribution, population density), or natural environmental conditions (such as climate, precipitation). For example, in a city, for different types of areas such as green spaces, transportation roads, water bodies, and buildings, the spatio-temporal change laws of variables such as temperature, humidity, and air quality may be significantly different. Spatio-temporal pattern heterogeneity poses higher requirements for sampling design. Since the spatio-temporal patterns of different sub-units within a region may vary significantly, traditional sampling methods based on the assumption of a single spatio-temporal pattern are difficult to accurately capture the local change characteristics of the variable. This limitation may lead to problems such as unbalanced sampling point layout and accumulation of time-series monitoring errors.

[0005] In summary, the main defect of existing sampling methods is that they usually assume that the spatio-temporal change pattern of environmental variables within a region is consistent, while ignoring the existence of multi-spatio-temporal patterns and their impact on sampling design. The heterogeneity characteristics of multi-spatio-temporal patterns determine that sampling methods need to have the ability to flexibly adapt to the internal structural differences of the region to effectively capture the true characteristics and complex change laws of variables within the region. Therefore, designing a sampling method that can take into account spatio-temporal pattern heterogeneity is of great significance for improving the comprehensiveness, accuracy, and resource utilization efficiency of sampling schemes. SUMMARY OF THE INVENTION

[0006] The object of the present invention is: to solve the problem that the existing sampling methods do not fully consider the spatio-temporal pattern heterogeneity of environmental variables in complex geospatial environments, and to propose a sampling method that takes into account spatio-temporal pattern heterogeneity, including the following steps:

[0007] S1. Obtain multi-source environmental data with spatio-temporal attributes, and perform preprocessing operations to obtain a spatio-temporal data set;

[0008] S2. Based on the dynamic mode decomposition technology, perform spatio-temporal pattern recognition and analysis on the spatio-temporal data set, extract spatio-temporal change characteristic parameters in the study area, and divide the study area into multiple geographical sub-units with spatio-temporal change pattern heterogeneity characteristics according to the spatio-temporal change characteristic parameters;

[0009] S3. Adopt grid generation technology to generate candidate points within the geographical sub-units, select some candidate points as the initially deployed sampling point set, and regard the unselected candidate points as un-sampled points;

[0010] S4. Construct a distributed spatio-temporal prediction model set, where each geographical sub-unit matches an independent spatio-temporal prediction model, use the sampling points within the sub-unit to perform spatio-temporal prediction on the un-sampled points, and calculate the spatio-temporal prediction error of the un-sampled points within the sub-unit;

[0011] S5. Based on the dynamic error feedback mechanism, dynamically determine the positions of newly added sampling points according to the spatio-temporal prediction errors of the un-sampled points within the sub-unit, as well as the preset sampling frequency and sampling quantity, and update the sampling point set within the sub-unit at the same time;

[0012] S6. Through a multi-round multi-parameter joint iterative optimization process, dynamically update the spatio-temporal prediction model parameters matched by the sub-units. If the sampling conditions meet the set stop conditions, output the updated sampling point set and generate the final sampling layout plan; otherwise, use the updated sampling point set to return to step S4 and continue the loop iteration process until the sampling stop conditions are met.

[0013] Further, the data preprocessing includes: data cleaning, outlier correction, data format unification, and spatio-temporal consistency correction.

[0014] Further, the selection of the initially deployed sampling point set is obtained by performing random sampling, uniform sampling, or inhibitory sampling design on the candidate points. The inhibitory sampling design preferentially selects candidate points with higher information entropy as the initial sampling points.

[0015] Further, the spatio-temporal prediction model is expressed as:

[0016] Z(s,t) = β0 + X T β + Y(s,t) + ε(s,t),

[0017] Y(s,t) = C0 + cXt +ε(s,t) = ρY(s,t - 1)+η(s,t),

[0018]

[0019] where Z(s,t) represents the actual observed value of the variable at spatial point s at time t, β0 represents the global intercept, β represents the regression coefficient vector corresponding to the predictor variables, X represents the spatially varying covariates, ε(s,t) represents the error term independent of spatial location, Y(s,t) represents the Gaussian random field describing the continuous spatial index of Z(s,t), C0 represents the global intercept or constant term, c represents the linear regression coefficient, ρ represents the temporal autocorrelation coefficient, Y(s,t - 1) represents the Gaussian random field describing the continuous spatial index of Z(s,t - 1), Z(s,t - 1) represents the actual observed value of the variable at site s at time t - 1, and η(s,t) represents the residual random term, represents a Gaussian distribution with mean 0 and variance , represents a Gaussian distribution with mean 0 and variance , represents the variance that does not vary spatially, S η represents the covariance matrix related to spatial correlation.

[0020] Furthermore, the covariance function of the Gaussian random field is expressed as:

[0021]

[0022] where Cov(Y(s i ,t),Y(s j ,t)) represents the covariance between Y(s i ,t) and Y(s j ,t), Y(s i ,t) and Y(s j ,t) respectively represent the Gaussian random fields describing the continuous spatial indices of Z(s i ,t) and Z(s j ,t), Z(s i ,t) and Z9s j ,t) respectively represent the actual observed values of the variables at sites s i and s j at time t, v represents the parameter controlling the smoothness, Γ() represents the gamma function, u = ||s i - s j || represents the Euclidean distance between s i and s j in space, s i represents the i-th site, s j represents the j-th site, represents the decay rate of spatial correlation, K v represents the second-order Bessel function.

[0023] Furthermore, a Gaussian random field is discretized into a Gaussian Markov random field by using a stochastic partial differential equation, and an integrated nested Laplace approximation inference method is used to estimate the parameters of the spatio-temporal prediction model and infer the distribution, so as to generate the probability distribution of the target variable in the prediction region.

[0024] Furthermore, the objective function of the spatio-temporal prediction model is to minimize the spatio-temporal prediction error of the sub-units.

[0025] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above sampling method considering spatio-temporal pattern heterogeneity is realized.

[0026] The present invention also provides an electronic device, including a processor and a memory, the processor is connected to the memory. Wherein, the memory is used to store a computer program, the computer program includes computer-readable instructions, and the processor is configured to call the computer-readable instructions to execute the above sampling method considering spatio-temporal pattern heterogeneity.

[0027] The beneficial effects brought by the technical solution provided by the present invention are:

[0028] The present invention proposes a dynamic sampling optimization scheme. Initial sampling points are selected through non - adaptive design, and an initial spatio - temporal prediction model is constructed based on representative data, providing a scientific starting point for subsequent dynamic optimization sampling and ensuring the rationality and balance of the layout of the initial sampling points. The present invention uses the method based on Stochastic Partial Differential Equation (SPDE) and Integrated Nested Laplace Approximation (INLA) for spatio - temporal prediction modeling. By accurately describing the characteristics of the Gaussian random field in the target area, this method effectively captures the multi - spatio - temporal variation patterns caused by spatial heterogeneity, temporal non - stationarity, and spatio - temporal interaction, significantly improving the modeling accuracy while optimizing the computational efficiency. Aiming at the spatio - temporal pattern heterogeneity of the study area, the present invention constructs multiple spatio - temporal prediction models to match the diverse pattern characteristics of different geographical sub - units. By decoupling the spatio - temporal pattern differences between different sub - units, accurate modeling of multiple regional sub - units is finally achieved. The present invention proposes a technical solution for realizing adaptive sampling and optimized layout by using a dynamic error feedback mechanism, dynamically adjusting the positions of sampling points according to the prediction errors of each regional unit, iteratively optimizing the sampling layout round by round, and improving the rationality of the spatial distribution of sampling points and the representativeness of sampling results. The technical solution of the present invention effectively solves the problem of spatio - temporal pattern heterogeneity caused by geographical elements such as water bodies, buildings, green spaces, as well as social and economic activities and land use changes in complex geographical space environments. It significantly improves the sampling efficiency and layout accuracy in the process of accurate modeling and adaptive optimization sampling of multi - spatio - temporal patterns, avoids the error accumulation caused by traditional sampling methods ignoring local change characteristics, and provides an efficient and reliable technical support for spatial data collection, monitoring, and prediction in complex geographical environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is the overall flowchart of the sampling method considering spatio - temporal pattern heterogeneity in the embodiment of the present invention;

[0030] Figure 2 is the flowchart of constructing an independent spatio - temporal prediction model based on Bayesian theory in the embodiment of the present invention;

[0031] Figure 3 is the block diagram of an electronic device in an exemplary embodiment of Embodiment 1 of the present invention;

[0032] Figure 4 is the schematic diagram of the set of candidate points of the centroid coordinates of the grid in the study area in the embodiment of the present invention.

[0033] Figure 5 is the schematic diagram of the spatial distribution of sampling points by different sampling methods in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0035] Glossary of terms:

[0036] Goal orientation: Each task will have its own specific main goal. The present invention proposes a general framework for spatial sampling point planning to elaborate the technical processes of spatial sampling points and layout points. The ultimate goal is to select a finite number of sampling points and layout points from an infinite number of spatial positions, not only minimizing the spatio-temporal prediction of the unlaid area for the layout points globally, but also minimizing the spatio-temporal prediction errors for multiple sub-units.

[0037] The flowchart of the sampling method considering spatio-temporal pattern heterogeneity in the embodiments of the present invention is as Figure 1 , and specifically includes the following steps:

[0038] S1. Obtain multi-source environmental data with spatio-temporal attributes, and perform preprocessing operations on the data to generate a normalized spatio-temporal data set.

[0039] The multi-sources can be remote sensing images, historical observation data, meteorological data, and other auxiliary data, and environmental monitoring station data, including the spatial location, observation time, and observation indicators of the stations.

[0040] Data preprocessing includes data cleaning, outlier correction, data format unification, and spatio-temporal consistency correction, etc. The collected raw data usually has quality and format problems and needs to be regularized through a unified preprocessing process. The data cleaning part uses rule or model methods to identify and clean missing values, noise, and outliers to ensure the integrity of the data. The format conversion part converts different source data into a unified format. Through time interpolation and spatial resampling methods, the data resolution, time span, and reference frame are made consistent to generate a normalized spatio-temporal data set. The data is structurally processed according to the goal orientation.

[0041] The outlier correction method is as follows:

[0042]

[0043] Among them, is the sample set within the time window t j represents the jth time window,[[ID=3B]] represents the set of time windows, w j is the spatial distance weight of

[0044] S2. Based on the dynamic mode decomposition technology, perform spatio-temporal pattern recognition and analysis on the spatio-temporal data set, extract spatio-temporal change characteristic parameters within the research area, and divide the research area into multiple geographical sub-units with significant spatio-temporal change pattern heterogeneity characteristics according to the spatio-temporal change characteristic parameters.

[0045] Based on the Dynamic Mode Decomposition (DMD) technique, key spatio-temporal feature parameters are extracted from the normalized spatio-temporal dataset. By decomposing the spatio-temporal data matrix into eigenmodes (temporal mode and spatial mode), the dynamic spatio-temporal change patterns of different sub-units within the study area are identified.

[0046] The spatio-temporal data matrix is expressed as where \(t\) is the time step, \(m\) is the spatial variable, and \(n\) is the time variable. A sequence of data matrices is constructed within the time window:

[0047] \(X = [x_1, x_2, \cdots, x_{n_t}]\), \(X' = [x_2, x_3, \cdots, x_{n_t + 1}]\), n-1 , \(X' = [x_2, x_3, \cdots, x_{n_t + 1}]\), n ,

[0048] where \(X\) and \(X'\) represent the current state and the shifted state respectively. The spatio-temporal matrix is decomposed using Singular Value Decomposition (SVD):

[0049] \(X = U\Sigma V^T\) T ),

[0050] where \(U\) and \(V\) T are the left and right singular vectors respectively, and \(\Sigma\) is the singular value matrix. A low-rank approximation of the eigenmode is constructed:

[0051] \(A\) k = U - X'V\Sigma^{-1} -1 ),

[0052] and by calculating the eigenvalues and eigenvectors, the dominant dynamic modes are extracted to obtain the reconstruction result of the spatio-temporal change. According to the results of the spatio-temporal feature analysis, combined with the modal feature weights generated by the dynamic mode decomposition, the study area is divided into multiple geographical sub-units with significantly different dynamic features. The division criterion is the heterogeneity of high-frequency and low-frequency modes, while referring to the characteristic parameters of the local space. The modal division formula is:

[0053]

[0054] where \(n\) is the total number of data points, \(k\) is the number of cluster centers, \(X_i\) i is the feature vector of the \(i\)-th data point, \(C_j\) j represents the \(j\)-th cluster center, and \(w_{ij}\) ij indicates whether the data point \(X_i\) i is assigned to the cluster center \(C_j\) j .

[0055] S3. Adopt grid generation technology to generate a set of candidate sampling points within a geographical subunit, and in combination with the initial sampling design, select some of the candidate points as the set of initially deployed sampling points, and regard the unselected candidate points as unsampled points.

[0056] Divide the study area into multiple subunits according to the spatio-temporal heterogeneity characteristics, and further divide each subunit into multiple grid cells. Within each grid cell, several candidate points are generated to form a set of candidate locations covering the entire area. These candidate points will serve as the preliminary layout and be screened and adjusted through subsequent optimization algorithms to determine the final sampling point distribution. The spatial and temporal resolutions of the grid division can be flexibly set according to specific analysis objectives to meet the requirements of different application scenarios.

[0057] Based on the generated set of candidate points, conduct initial sampling. By certain rules or methods, select a group of initial sampling points to construct an initial sampling set. The available initial sampling strategies include non-adaptive sampling methods such as random sampling, uniform sampling, and inhibitory sampling.

[0058] S4. Construct a set of distributed spatio-temporal prediction models, where each geographical subunit is matched with an independent spatio-temporal prediction model to fully characterize the specific spatio-temporal pattern dependence relationships within the subunit; use the sampling points within the subunit to perform spatio-temporal prediction on the unsampled points, and calculate the spatio-temporal prediction errors of the unsampled areas within the subunit.

[0059] For each subunit, construct an independent spatio-temporal prediction model based on Bayesian theory to fully characterize the specific spatio-temporal pattern dependence relationships within the subunit. Refer to Figure 2 , Figure 2 which is the flow chart of constructing an independent spatio-temporal prediction model based on Bayesian theory in the embodiments of the present invention. The model formula is as follows:

[0060] Z(s,t)=β0+X T β+Y(s,t)+ε(s,t),

[0061] Y(s,t)=C0+cX t +ε(s,t)=ρY(s,t - 1)+η(s,t),

[0062]

[0063] where Z(s,t) represents the actual observed value of the variable at spatial point s at time t, s = s1, …, s n , D∈R 2It is assumed that the study area D is a fixed subset in two-dimensional space, and t is time (in months); β0 represents the global intercept (constant term), which represents the overall baseline level of the target variable, and β represents the regression coefficient vector corresponding to the predictor variables; X represents the spatially varying covariates; ε(s,t) represents the error term independent of the spatial position, usually Gaussian white noise; Y(s,t) represents the Gaussian random field that describes the continuous spatial index of Z(s,t); C0 represents the global intercept or constant term; c represents the linear regression coefficient; ρ represents the temporal autocorrelation coefficient; Y(s,t - 1) represents the Gaussian random field that describes the continuous spatial index of Z(s,t - 1); Z(s,t) represents the actual observed value of the variable at site s at time t; η(s,t) represents the residual random term, which is used to characterize the spatio-temporal random effects of the latent variable, and η(s,t) is independent in time and follows a Gaussian distribution in space denotes a Gaussian distribution with mean 0 and variance ; denotes a Gaussian distribution with mean 0 and variance ; denotes the variance that does not vary spatially, S η represents the covariance matrix related to space.

[0064] The covariance function of the Gaussian random field is expressed as:

[0065]

[0066] where Cov(Y(s i [[ID=2))],t),Y(s j ,t)) represents the covariance between Y(s i ,t) and Y(s j ,t), Y(s i ,t) and Y(s j ,t) respectively represent the Gaussian random fields that describe the continuous spatial indices of Z(s i ,t) and Z(s j ,t), Z(s i ,t) and Z(s j ,t) respectively represent the actual observed values of the variables at sites s i and s j at time t, v represents the parameter that controls the smoothness, Γ() represents the gamma function, u = ||s i - s j || represents the Euclidean distance between s i and s j in space, s i represents the i-th site, s j represents the j-th site, represents the decay rate of spatial correlation, Kv represents the second-order Bessel function.

[0067] The parameters to be estimated in the spatio-temporal model are Except for and v, other parameters have conjugate prior distributions, that is, given the prior distribution, β, ρ, can all obtain the standard posterior distribution that meets the conditions.

[0068] The Gaussian random field is discretized into a Gaussian Markov random field by using a stochastic partial differential equation, and the integrated nested Laplace inference is used to solve the parameter estimation and distribution inference in the spatio-temporal prediction model, and generate the distribution probability of the target variable in the prediction area.

[0069] In the case of multi-spatio-temporal patterns, the problem faced is that there are multiple spatio-temporal change patterns in the environmental variables of the study area, and a single spatio-temporal pattern model cannot be used to mine the spatio-temporal models of multiple regions. The goal of the multi-pattern spatio-temporal adaptive sampling framework that takes into account spatio-temporal heterogeneity is to select a finite set of sampling point positions from the set of potential candidate points within the study area, so that these sampling points can minimize the spatio-temporal prediction error of the unlaid area globally, and at the same time meet the requirements of minimizing the spatio-temporal prediction error of multiple sub-units.

[0070] The multi-spatio-temporal prediction model consists of multiple spatio-temporal prediction models with different spatio-temporal change patterns, and each model represents the change law of a sub-unit or a specific spatio-temporal pattern. The objective function of the multi-spatio-temporal prediction model is to minimize the joint prediction error of multiple spatio-temporal prediction models with different spatio-temporal change patterns.

[0071] S5. Based on the dynamic error feedback mechanism, according to the spatio-temporal prediction error distribution results of geographical sub-units, as well as the preset sampling frequency and sampling quantity, dynamically judge the optimal positions of newly added sampling points, and at the same time update the sampling point set within the sub-unit.

[0072] Based on the spatio-temporal prediction model, the present invention designs a dynamic adaptive sampling optimization method based on the dynamic error feedback mechanism. By analyzing the spatio-temporal prediction error distribution of geographical sub-units, combined with the preset sampling frequency and sampling quantity, dynamically judge the optimal positions of newly added sampling points, and update the sampling point set.

[0073] S6. Through multiple rounds of multi-parameter joint iterative optimization processes, dynamically update the spatio-temporal prediction model parameters matched by the sub-units to realize the update of the spatio-temporal models of geographical sub-units. According to the set stopping criterion, if the sampling conditions are met, output the optimized sampling point set and generate the final sampling layout plan; otherwise, use the updated sampling point set to return to step S4 and continue the loop iteration process until the sampling termination conditions are met.

[0074] Through multiple rounds of multi-parameter joint iterative optimization, the present invention continuously updates the spatio-temporal prediction model parameters for geographical sub-unit matching, improving the accuracy and generalization ability of the model. Combining with a dynamic error feedback mechanism, the multi-round optimization dynamically adjusts the layout of sampling points. The set conditions are as follows: the size of the sampling point set reaches a preset standard; there are no more potential sampling points; the improvement amplitude of the prediction accuracy reaches the convergence condition.

[0075] According to the updated model, calculate the spatio-temporal prediction error of the current sampling point set E t , evaluate the model performance of the geographical sub-unit, and determine whether the sampling conditions meet the preset sampling termination criterion. The error function is:

[0076]

[0077] where E represents the spatio-temporal prediction error, which is the overall weighted average error (global error); E k is the average prediction error of the k-th sub-unit, calculated based on all sampling points within it; k represents the number of sub-units, and the formula divides the entire research area into k sub-units, and a separate error is calculated within each sub-unit; ω k represents the weight of the sub-unit; Z(s i , t) represents the true value of the spatial point s i at time t; represents the predicted value of the spatial point s i at time t; n k represents the number of sampling points of the sub-unit.

[0078] Preset error threshold ∈ th and parameter change threshold δ th , and the sampling termination criterion needs to meet two conditions:

[0079] Condition 1: E < ∈ th ; Condition 2: |Ξ (i+1) -Ξ (i) | < δ th , Ξ (i+1) represents the parameter after the (i + 1)-th iteration, and Ξ (i) represents the parameter after the i-th iteration. If both are satisfied, the iteration is terminated; otherwise, new sampling points are added continuously.

[0080] In an exemplary embodiment, there is provided a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described sampling method considering spatio-temporal pattern heterogeneity.

[0081] Please refer to Figure 3, in an exemplary embodiment, it further includes an electronic device, which includes at least one processor, at least one memory, and at least one communication bus.

[0082] Wherein, a computer program is stored on the memory, the computer program includes computer-readable instructions, and the processor calls the computer-readable instructions stored in the memory through the communication bus to execute the above-mentioned sampling method that takes into account spatio-temporal pattern heterogeneity.

[0083] Based on the above technical solutions, the key technical points of the present invention are as follows:

[0084] By selecting initial sampling points through non-adaptive design, a reasonable initial layout is provided for the spatio-temporal prediction model, so as to more accurately capture the spatio-temporal change characteristics in the region; combining the Stochastic Partial Differential Equation (SPDE) with the Integrated Nested Laplace Approximation (INLA) method to construct an efficient spatio-temporal prediction model to achieve accurate modeling of the Gaussian random field characteristics of the target region; aiming at spatio-temporal pattern heterogeneity, by matching the diversity characteristics of different geographical sub-units, a spatio-temporal prediction model with multiple sub-units is constructed; using a dynamic error feedback mechanism to perform multiple rounds of optimization and adjustment on the sampling point layout to adaptively reduce the spatio-temporal prediction error; integrating the multi-spatio-temporal pattern characteristics in the region to solve the sampling error problem caused by spatial heterogeneity, temporal non-stationarity and interaction effects in a complex geospatial environment, and finally realizing an efficient and flexible optimized layout of sampling points.

[0085] To verify the beneficial effects of the technical solutions of the present invention, the method of the present invention (MR-ASTS) is compared with the traditional sampling point layout method (ASTS) that does not take into account spatio-temporal pattern heterogeneity, where the target variable is PM 2.5 , and the data period is from January 1, 2021 to December 31, 2021. The data is divided into 5km grids, and the centroid coordinates of the pixel are extracted as the candidate point set and valued. The present invention first identifies 3 sub-units A1, A2, A3 with different spatio-temporal patterns, as Figure 4 shown. The candidate point set of the centroid coordinates of the grid points in the study area in the embodiment is as Figure 4 grid points, where there are 71, 85, and 83 candidate points for A1, A2, and A3. To stabilize the variance that increases with the mean value and make the distribution of PM 2.5 data approximate to a normal distribution, the logarithmic transformation rule is used.

[0086] Compared with the traditional method that does not take into account spatio-temporal pattern heterogeneity, the prediction errors of the method of the present invention for the unlaid points under different numbers of sampling points are shown in Table 1. The layout schemes generated by the method of the present invention and the traditional method are as Figure 5As shown. Table 1 shows the performance comparison results between the method of the present invention and the traditional method under different sampling scales. The metrics include root mean square error (RMSE), mean absolute error (MAE), mean square error (MSE), and coefficient of determination (R 2 ). It can be seen from the data that the method of the present invention is superior to the traditional method in all metrics. For example, when Size is 10, the RMSE of MR-ASTS is reduced by 20.78% compared to ASTS, the MAE is reduced by 4.79%, the MSE is reduced by 49.48%, and R 2 is increased by 4.88%; when Size is 14, the RMSE is reduced by 2.75%, the MAE is reduced by 3.08%, the MSE is reduced by 13.79%, and R 2 is increased by 1.36%. Generally speaking, the method of the present invention can better capture the spatio-temporal pattern heterogeneity, and it is significantly superior to the traditional method in terms of error control and prediction accuracy, and has higher practicability and adaptability.

[0087] Table 1 Comparison Table of Prediction Results

[0088]

[0089] Compared with the prior art, the advantage of the present invention lies in proposing a spatial sampling method that takes into account spatio-temporal pattern heterogeneity, and coordinates the local change characteristics of variables and the spatio-temporal representativeness of the overall region. Based on the multi-region spatio-temporal adaptive sampling framework, the present invention effectively solves the sampling layout problem of the monitoring region under multi-spatio-temporal pattern conditions. By introducing a spatio-temporal dynamic prediction model that combines stochastic partial differential equations and integrated nested Laplace approximation, the present invention can predict the spatial field of the unlaid region, and adopts a multi-region adaptive sampling algorithm that integrates the information gain function to gradually optimize the sampling point layout. The experimental results show that the method of the present invention exhibits excellent spatio-temporal representativeness in the sampling layout strategy, effectively improves the sampling efficiency and modeling accuracy, and fully meets the monitoring requirements of multi-spatio-temporal patterns in complex geographical environments.

[0090] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A sampling method considering the spatio-temporal pattern heterogeneity, characterized in that, It includes the following steps: S1. Obtain multi-source environmental data with spatio-temporal attributes, and perform preprocessing operations to obtain a spatio-temporal data set; S2. Based on the dynamic mode decomposition technology, perform spatio-temporal pattern recognition and analysis on the spatio-temporal data set, extract spatio-temporal change characteristic parameters within the study area, and divide the study area into multiple geographical sub-units with heterogeneous spatio-temporal change pattern characteristics according to the spatio-temporal change characteristic parameters; S3. Adopt grid generation technology to generate candidate points within the geographical sub-units, select some candidate points as the initial sampling point set for layout, and regard the unselected candidate points as unsampled points; S4. Construct a distributed spatio-temporal prediction model set, where each geographical sub-unit matches an independent spatio-temporal prediction model, use the sampling points within the sub-unit to perform spatio-temporal prediction on the unsampled points, and calculate the spatio-temporal prediction error of the unsampled points within the sub-unit; S5. Based on the error feedback mechanism, according to the spatio-temporal prediction error of the unsampled points within the sub-unit, as well as the preset sampling frequency and sampling quantity, judge the positions of the newly added sampling points, and update the sampling point set within the sub-unit at the same time; S6. Through the joint iterative optimization process of multiple model parameters, dynamically update the parameters of the spatio-temporal prediction model matched by the sub-unit. According to the set stopping criterion, if the sampling condition meets the set stopping condition, output the updated sampling point set and generate the final sampling layout plan; Otherwise, use the updated sampling point set to return to step S4 and continue the loop iteration process until the sampling stop condition is met.

2. The sampling method considering the spatio-temporal pattern heterogeneity according to claim 1, characterized in that The data preprocessing includes: data cleaning, outlier correction, data format unification, and spatio-temporal consistency correction.

3. A sampling method considering the heterogeneity of spatio-temporal patterns according to claim 1, characterized in that The selection of the initial sampling point set for layout is obtained by random sampling, uniform sampling or inhibitory sampling design of the candidate points. The inhibitory sampling design preferentially selects candidate points with higher information entropy as the initial sampling points.

4. A sampling method considering the heterogeneity of spatio-temporal patterns according to claim 1, characterized in that The spatio-temporal prediction model is expressed as: Z(s,t) = β0 + X T β + Y(s,t) + ε(s,t), Y(s,t) = C0 + cX t + ε(s,t) = ρY(s,t - 1) + η(s,t), Among them, Z(s,t) represents the actual observed value of the variable of spatial point s at time t, β0 represents the global intercept, β represents the regression coefficient vector corresponding to the predictor variable, X represents the spatially varying covariate, ε(s,t) represents the error term independent of spatial position, Y(s,t) represents the Gaussian random field describing the continuous spatial index of Z(s,t), C0 represents the global intercept or constant term, c represents the linear regression coefficient, ρ represents the temporal autocorrelation coefficient, Y(s,t - 1) represents the Gaussian random field describing the continuous spatial index of Z(s,t - 1), Z(s,t - 1) represents the actual observed value of the variable of site s at time t - 1, and η(s,t) represents the residual random term. represents a Gaussian distribution with a mathematical expectation of 0 and a variance of . represents a Gaussian distribution with a mathematical expectation of 0 and a variance of . represents the variance that does not vary with space, S η represents the covariance matrix related to space.

5. A sampling method that takes into account the spatio-temporal pattern heterogeneity according to claim 4, characterized in that The covariance function of the Gaussian random field is expressed as: where, Cov(Y(s i ,t),Y(s j ,t)) represents the covariance of Y(s i ,t) and Y(s j ,t), Y(s i ,t) and Y(s j ,t) respectively represent Gaussian random fields describing the continuous spatial indices of Z(s i ,t) and Z(s j ,t), Z(s i ,t) and Z(s j ,t) respectively represent the actual observed values of the variables at sites s i and s j at time t, v represents the parameter controlling the smoothness, Γ() represents the gamma function, u = ||s i - s j || represents the Euclidean distance between s i and s j in space, s i represents the i-th site, s j represents the j-th site, represents the decay rate of spatial correlation, K v represents the second-order Bessel function.

6. The sampling method considering spatio-temporal pattern heterogeneity according to claim 5, wherein Use a stochastic partial differential equation to discretize the Gaussian random field into a Gaussian Markov random field, and use the integrated nested Laplace approximation inference method to estimate and infer the parameters of the spatio-temporal prediction model, and generate the probability distribution of the target variable in the prediction area.

7. The sampling method considering spatio-temporal pattern heterogeneity according to claim 1, wherein The objective function of the spatio-temporal prediction model is to minimize the spatio-temporal prediction error of the sub-unit.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method described in any one of claims 1-7 is executed.

9. An electronic device, characterized in that: It includes a processor and a memory, the processor is connected to the memory, wherein, the memory is used to store a computer program, the computer program includes computer-readable instructions, and the processor is configured to call the computer-readable instructions to execute the method described in any one of claims 1-7.

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