An indoor temperature and humidity spatial data prediction method fusing spatial interpolation and graph convolution network

Abstract

The application discloses an indoor temperature and humidity spatial data prediction method fusing spatial interpolation and graph convolution network, and relates to the fields of smart cities and environmental monitoring.The method comprises the following steps: acquiring indoor multi-point temperature and humidity data measured by a sensor and corresponding monitoring marker point spatial position information; using the temperature and humidity data, the spatial position information and time dimension features of the marker points as inputs of Kriging interpolation to generate linear prediction values of temperature and humidity of part of unmarked points; constructing a multiple linear regression model with the Kriging prediction results, the measured data of the marker points, time dimension features, spatial features and external meteorological data as independent variables and the target temperature and humidity values as a dependent variable to perform multidimensional fitting on the Kriging interpolation results; using the linear prediction values output by the regression model and other features to construct a feature matrix, and using the feature matrix and an adjacency matrix as inputs of a graph convolution network to generate a three-dimensional spatial distribution of indoor temperature and humidity.The application can realize high-precision indoor spatial data prediction.

Description

Technical Field

[0001] This invention relates to the field of indoor space data monitoring in smart cities, and in particular to a method for predicting indoor temperature and humidity spatial data by integrating spatial interpolation and graph convolutional networks. Background Technology

[0002] Currently, the construction of smart cities is a medium- and long-term development goal in my country. The digitalization and intelligentization of urban buildings urgently require the installation of advanced indoor environmental monitoring systems to track, analyze, and regulate microenvironmental factors such as indoor air quality, temperature, and humidity in real time. This can not only improve the comfort and health level inside buildings but also enable early warning and forecasting of indoor disasters such as fires through data analysis.

[0003] Traditional indoor environmental monitoring technologies typically employ single or a small number of sensors, deployed at building vents or other easily accessible locations to monitor the environment of the entire indoor space. However, this low-data-volume, limited-point-capacity approach makes it difficult to accurately monitor and analyze the microenvironment of specific locations, especially in irregular spaces where complex spatial structures exacerbate the limitations. Such methods cannot cover environmental parameter monitoring in all areas within a building, failing to meet the refined management requirements of smart buildings.

[0004] With the development of artificial intelligence, more deep learning technologies and spatial interpolation methods are being applied to the field of spatial data monitoring, striving to achieve more comprehensive spatial data acquisition. Kriging interpolation, a classic geostatistical modeling method, is an optimal unbiased interpolation method based on statistical theory. This method uses data from known points as a basis, combined with spatial location and spatial variation characteristics, to provide estimates for unmeasured points while quantifying the uncertainty of the estimates. However, Kriging relies heavily on spatial autocorrelation, and its basic assumption is a regular, flat, and continuous grid estimation. For irregular spaces, boundary effects exist, and distance calculations in irregular spaces need to consider spatial geometry; complex geometries make it difficult to accurately model spatial autocorrelation. Graph convolutional neural networks comprehensively consider the global connectivity and local dependencies of measurement points, directly modeling the non-uniformity and irregular physical structure of space, and can better capture the correlations in complex spaces. However, the effectiveness of graph convolutional neural networks depends on large-scale data for model training and has high computational resource requirements.

[0005] In summary, existing methods for predicting indoor temperature and humidity based on spatial data have the following problems:

[0006] (1) Traditional environmental monitoring technologies cannot perform detailed monitoring and management of the entire indoor space;

[0007] (2) In irregular spaces, complex geometry makes it difficult to accurately model using traditional methods;

[0008] (3) Traditional Kriging methods cannot handle irregular spaces with boundary effects and complex geometric structures;

[0009] (4) Graph convolutional networks require a large amount of data to train the model, and the effect is poor when the amount of data is insufficient.

[0010] To address the above problems, this invention discloses a method for predicting indoor temperature and humidity spatial data by integrating spatial interpolation and graph convolutional networks. Summary of the Invention

[0011] The present invention aims to solve the problem that traditional monitoring technologies are unable to achieve accurate and comprehensive monitoring and modeling in indoor spaces with complex geometric structures.

[0012] To achieve the above-mentioned technical objectives, the technical solution of the present invention is: a method for predicting indoor temperature and humidity spatial data by integrating spatial interpolation and graph convolutional networks, the specific steps of which are as follows:

[0013] Step 1) Distribute sensors at multiple points within the target study area, with each sensor corresponding to a measurement marker point. Record the temperature and humidity data of each sensor and its measurement time dimension characteristics. Simultaneously, acquire the spatial location information of all measurement marker points and preprocess the data;

[0014] Step 2) Using the data obtained in Step 1) as input for Kriging interpolation, a spatial covariance model is constructed by capturing the linear correlation of space to perform linear prediction of temperature and humidity at unmarked points.

[0015] Step 3) Construct a multiple linear regression model with Kriging linear prediction results, measured data of marked points, time dimension features, spatial features and external meteorological data as independent variables, and target temperature and humidity values ​​as dependent variables. Fit the Kriging interpolation results in multiple dimensions, and generate the processed spatial prediction values ​​of temperature and humidity based on the fitted multiple linear regression model.

[0016] Step 4) Perform residual fusion on the predicted values ​​after processing by the multiple linear regression model, and perform feature splicing with the measured temperature and humidity data of the marker points to construct a feature matrix. At the same time, based on the spatial location information of the marker points, obtain the geometric relationship and physical distance between each sensor node and construct an adjacency matrix.

[0017] Step 5) Build a graph convolutional network model. Input the feature matrix and adjacency matrix from step 4) into the graph convolutional network model for training. Use the fitted prediction model to obtain the three-dimensional spatial point and surface distribution of indoor temperature and humidity in the study area.

[0018] The present invention has the following beneficial effects:

[0019] 1. Compared with other indoor environmental monitoring methods, the multi-point distributed data acquisition method can obtain more comprehensive and detailed spatial point measurement data. It relies on the Kriging method to capture the best linear unbiased estimate of environmental spatial data and obtain the overall data distribution of the target area.

[0020] 2. Ambient temperature and humidity exhibit spatial autocorrelation, especially in irregular indoor scenes. Kriging interpolation is prioritized, and the correlation between temperature and humidity, as well as the influence of time dimension features, spatial features, and outdoor meteorological data variables, are considered. A multiple linear regression model is established to improve the prediction accuracy of the graph convolutional network for the target.

[0021] 3. By processing the initially estimated linear temperature and humidity values ​​and the measured temperature and humidity values, we can obtain fused data features, improve the positive quality of the data, enhance the estimation accuracy of the graph convolution model, and solve the problem of spatial distribution nonlinear prediction. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the overall technical route of the present invention;

[0023] Figure 2 This is a diagram showing the deployment of the multi-point distributed sensors according to the present invention.

[0024] Figure 3 The variation of point pairs in the present invention with xy = 0° and z = 0° is shown.

[0025] Figure 4 The variation of point pairs in the present invention with xy = 30° and z = 0°;

[0026] Figure 5 This illustrates the variation of the point pair in the present invention with directions xy = 60° and z = 0°.

[0027] Figure 6 This illustrates the variability of the point pair in the present invention with xy = 90° and z = 0°.

[0028] Figure 7 This illustrates the variation of the point pair in the present invention with directions xy = 120° and z = 0°.

[0029] Figure 8 This illustrates the variation of the point pair in the present invention with directions xy = 150° and z = 0°.

[0030] Figure 9 This illustrates the variation of the point pair in the present invention with directions xy = 180° and z = 0°.

[0031] Figure 10 This is a three-dimensional point data distribution map of the spatial prediction results of this invention;

[0032] Figure 11 This is a three-dimensional surface data distribution diagram of the spatial prediction results of this invention. Detailed Implementation

[0033] Combination Figure 1 The technical approach adopted in this invention is as follows: First, temperature and humidity data of marked points in the target study area are acquired and estimated using the Kriging interpolation method to obtain linear prediction values. Then, based on these prediction results, a multiple linear regression model is constructed to fit the linear changes in temperature and humidity in multiple dimensions. Finally, a graph convolutional neural network is used to process the spatial data to further obtain the comprehensive point-area distribution of indoor space temperature and humidity, achieving accurate prediction. The specific implementation includes the following steps:

[0034] Step 1) Distribute sensors at multiple points throughout the target study area, with each sensor corresponding to a measurement marker point, to acquire indoor temperature and humidity data, record the measurement time dimension characteristics, and perform data preprocessing; combined with Figure 2 The following describes the multi-point distributed sensor deployment: For example, taking the Satellite Imagery Cloud Service Research Laboratory of the Guangxi Key Laboratory of Spatial Information and Surveying and Mapping as the research area, its spatial information is x = 7.4m, y = 8.75m, z = 3m. Sensors are arranged in a 4*5 matrix on the xy plane; sensors are arranged in a 4*4 matrix on two sides of the zy and zx planes; and sensors with random spatial parameters xyz are arranged in the central area of ​​the space. The total number of measurement markers is 60. Then, the data is uploaded to the server for data storage and subsequent processing via LoRa wireless communication technology. The data preprocessing includes: handling missing values, smoothing, denoising, and normalizing the temperature and humidity data from each sensor; specifically as follows: for missing values ​​in the temperature and humidity data, a combination of interpolation and mean imputation is used to ensure data integrity; to eliminate noise in the data, exponential smoothing is used for data smoothing; since the fitting effect of the graph convolutional network is closely related to the data quality, the spatial location information and temperature and humidity data need to be normalized; the spatial coordinates of the marker points are scaled to the [0, 1] interval; at the same time, the temperature and humidity values ​​have large differences in range, so they need to be normalized to [0, 1] respectively to eliminate the difference in dimensions and ensure data consistency.

[0035] Step 2) When performing Kriging interpolation, it is necessary to capture the spatial correlation between pairs of marked points. First, the distance between the pairs is calculated and directionally grouped. Then, the spatial variability in different directions is calculated and analyzed using a semi-variogram to identify the strength of the correlation in each direction. Directions with strong correlations are determined as primary axes, and directions with weak correlations are determined as secondary axes. Finally, based on the constructed spatial covariance model, linear interpolation is performed to predict the temperature and humidity of unmarked points. The specific steps are as follows:

[0036] Calculate the Euclidean distance d between each pair of marked points in the horizontal direction. xy The height difference d in the vertical direction z To obtain the distance between points, the formula is as follows:

[0037]

[0038] d z =|z i -z j |

[0039] Where, x i y i and x j y j These are the marker points P. i and P j In the XY plane coordinates, z i and z j This refers to the sensor deployment height. Intervals are grouped based on the distance between points.

[0040] After completing the distance grouping, for irregular indoor spaces, the marker points need to be further grouped by region based on the distance grouping, and directions are defined based on geometric features, distances between adjacent points, and angles. Specifically, directions are defined every 15° on the XY plane, ranging from 0° to 180°, for a total of 13 directions. Then, seven different angles are defined on the Z-axis perpendicularly: 0°, 15°, 30°, 45°, 60°, 75°, and 90°. Combining the XY plane directions and Z-axis angles, anisotropy analysis is performed on different directions in three-dimensional space.

[0041] Based on the grouping, the semivariogram of each pair of marked points is calculated to analyze spatial correlation. First, the semivariogram of point pairs (x, y, y) in different directions is calculated separately. i x j The interpolation square of the temperature and humidity values ​​[z(x)] i )-z(x j )] 2 , where z(x) is the temperature or humidity value of the marker point x. For a given distance h, the squared mean of the differences between all pairs of points at a distance h is calculated to determine the semivariogram, as shown in the following formula:

[0042]

[0043] Wherein, γ(h k ) is a distance of h k The semivariogram values ​​between point pairs, N(h) k ) is a distance of h k The number of point pairs.

[0044] Based on the calculated semivariogram values, an empirical semivariogram is plotted for each direction, and fitted using a Gaussian model, as shown below:

[0045]

[0046] Then, by comparing the variability in various directions, the principal and secondary axes are determined, specifically in conjunction with... Figures 3-9 This is an empirical semi-variogram of different directional groupings in this invention, illustrating how the variability of spatial data changes with distance and direction. Figure 3 It represents the variability of a point with directions xy = 0° and z = 0°; Figure 4 It represents the variability of a point with directions xy = 30° and z = 0°; Figure 5 It represents the variability of a point with directions xy = 60° and z = 0°; Figure 6 It represents the variability of a point with directions xy = 90° and z = 0°; Figure 7 It represents the variation of a point with directions xy = 120° and z = 0°; Figure 8 It represents the variation of a point with directions xy = 150° and z = 0°; Figure 9 This describes the variability of a point along directions xy = 180° and z = 0°. By comparing and analyzing the variability in different directions, the direction with stronger variability is selected as the principal axis, and the direction with weaker variability as the secondary axis. In one implementation, [the following is used]. Figure 4 The point-to-direction axis was selected as the principal axis. Figure 5 The point is used as the secondary axis in terms of direction.

[0047] By fitting the semi-variogram model, a spatial covariance model is defined, which reflects the following:

[0048]

[0049] For example, to obtain the positions of 20 measurement markers x1, x2, ..., x3 in the target region z=0 plane. n The covariance matrix is ​​obtained through the covariance function Cov(h).

[0050] For the target unmarked point, calculate its covariance with all known marked points and construct a covariance vector.

[0051] For example, the target region z=0 marker point P is calculated using the fitted semivariogram γ(h) and covariance function Cov(h). a With unmarked point P u The covariance values ​​are used to form a covariance vector.

[0052] Solve the linear system Cw = Cu Calculate the Kriging weights w to obtain the weights w of each known point to the unlabeled points. i .

[0053] Creating the Kriging Equation Calculate the linear prediction results of temperature and humidity for unmarked points in the indoor space, where Z(x) i (x) is a known point. i The temperature and humidity values, Z(x0) is the linear prediction result of temperature and humidity without x0 label, w i To assign x to each group i For x u The weighting coefficients.

[0054] Step 3) Using the Kriging linear prediction results, measured data at marked points, time dimension features, spatial features, and outdoor meteorological data as independent variables, and the target predicted temperature and humidity as dependent variables, a multiple linear regression model is used. Through the well-fitted multiple linear regression model, the predicted values ​​of Kriging interpolation and other independent variables are fitted in multiple dimensions to adjust the preliminary Kriging linear prediction results.

[0055] Step 4) Based on the multiple linear regression prediction results, calculate the residuals ∈ between the model's predicted values ​​and the measured values ​​at the marked points. i And correct the predicted values, residuals ∈ i Represented as:

[0056] ∈ i =Y i r -Y i p

[0057] Corrected forecast for:

[0058]

[0059] The residual-corrected prediction results are then concatenated with other features to form a complete feature matrix. Specifically, this involves adjusting the prediction results of multiple linear regression using residuals to generate residual-corrected prediction results, and then concatenating these results with other features such as temperature and humidity data based on actual measurements at marker points. For example, the spatial location information α of the marker points, the time dimension feature t, outdoor temperature β1, outdoor humidity β2, rainfall ε, and the processed temperature and humidity data predicted values ​​Y are combined. s Fuse complete feature matrix Ensure that all important spatial, temporal, meteorological features and temperature and humidity data are effectively integrated to provide a complete feature set for subsequent modeling.

[0060] Step 5) Build a graph convolutional network model. Input the feature matrix and adjacency matrix from Step 4) into the graph convolutional network model for training. Use the fitted prediction model to obtain the three-dimensional spatial point-area distribution of indoor temperature and humidity in the study area. The specific steps are as follows:

[0061] Based on the spatial location information of the marked points processed in step 2), the geometric relationships and physical distances between each sensor node are obtained, and an adjacency matrix is ​​constructed based on these distances.

[0062] A Gaussian decay function is used to adjust the weights based on the distance between nodes, providing a smooth transition. Define the weights. Where d ij σ represents the distance between nodes i and j. σ controls the distance decay rate; a larger σ results in slower weight decay, while a smaller σ results in faster weight decay. This is based on the distance d between all measured marker nodes. ij The adjacency matrix is ​​constructed using the Gaussian decay function. To address the issue of overlapping nodes, a minimum self-loop weight ε is set, and the adjacency matrix is ​​normalized. Balance the degree differences between different nodes.

[0063] Build a graph convolutional network model and convert the feature matrix and adjacency matrix As input to the Graph Convolutional Network (GCN), to ensure that the node's own features participate in the convolution, the adjacency matrix is ​​used. Adding it to the self-loop identity matrix I yields the adjacency matrix with self-loops. Based on the degree of each node Construct degree matrix And perform symmetric normalization to obtain For each layer l, through To achieve feature aggregation, where It is the weight matrix, which introduces the nonlinearity of the model through the nonlinear activation function σ = max(0, x), where x represents the result of the features of the l-th layer node after linear transformation and neighborhood aggregation.

[0064] Optimization is performed by defining the mean squared error (MSE) as the loss function, with the following formula:

[0065]

[0066] The gradient descent algorithm is used to minimize the loss, the network weights are updated, and the feature matrix G of the final output layer is obtained after multiple layers of graph convolution. (L) Represents the predicted temperature and humidity values ​​for each unlabeled node.

[0067] The fitted prediction model is used to obtain the predicted temperature and humidity values ​​of the unlabeled nodes. The predicted data and spatial location information are fused with the 3D reality model of the study area to obtain the 3D spatial point-area distribution of indoor temperature and humidity in the study area, as follows:

[0068] The distribution of 3D target point data is presented in a 3D scattered format. The 3D mapping position of each target point in the real-world 3D model is determined by its 3D coordinates (x, y, z). A color mapping function is used to map the temperature or humidity of the target point to a color to represent the data level. Specifically, as shown... Figure 10 The mapping distribution results of the point data for the target point show the spatial distribution of the point data.

[0069] The 3D target surface data distribution uses spatial slicing to predict temperature and humidity values. The spatial distribution of indoor temperature and humidity is rendered. The study area is divided into multiple xy-planes to construct multiple layers. Each layer generates a corresponding 3D model of the study area's x and y ranges using a lookup table function. Apply gradient color mapping Mapping to the corresponding color parameters, specifically as follows: Figure 11 The rendering mapping result of the spatial slice plane shows the spatial distribution of the surface data.

[0070] This invention proposes a spatial data prediction method for indoor temperature and humidity that integrates spatial interpolation and graph convolutional networks. This method effectively considers the correlation between temperature and humidity, as well as the influence of temporal, spatial, and outdoor meteorological data variables. It utilizes the Kriging spatial interpolation method and extracts deep spatial information features through graph convolutional networks to solve the problem of nonlinear spatial distribution prediction. Verification shows that the fusion method of spatial interpolation and graph convolutional networks can effectively capture the spatial characteristics of indoor temperature and humidity and better reflect the spatiotemporal three-dimensional point-to-surface distribution of indoor temperature and humidity.

[0071] As described above, the essence of this invention extends far beyond the specific details of the exemplary embodiments. Its core spirit and features can be implemented in various ways and are not limited to the examples currently presented. Therefore, the embodiments should be considered illustrative rather than restrictive. The scope of this invention is defined by the appended claims, which are intended to include all variations and implementations consistent with the principle of equivalence of the claims within their scope of protection. No illustrative markings in the claims should be construed as limiting the related claims.

[0072] It is worth noting that although this specification presents specific embodiments, those skilled in the art should recognize that these descriptions are merely for clarity, and the technical solutions in each embodiment can be appropriately combined to form other embodiments adapted to specific situations and materials, without departing from the spirit and scope of the invention. The essence of the invention is not limited to the specific embodiments disclosed; all embodiments formed by reasonable changes or equivalent substitutions within the spirit and scope of the invention are within the protection scope of the invention.

[0073] In summary, this invention aims to convey its core concepts and technical framework through exemplary examples, while emphasizing the flexibility of innovation and the breadth of application, ensuring that all variations and implementations that conform to its spirit and principles are covered.

Claims

1. A method for predicting indoor temperature and humidity spatial data by integrating spatial interpolation and graph convolutional networks, characterized in that, include: Step 1) Distribute sensors at multiple points within the target study area, with each sensor corresponding to a measurement marker point. Record the temperature and humidity data of each sensor and its measurement time dimension characteristics. At the same time, acquire the spatial location information of all measurement marker points and preprocess the data. Step 2) Using the data obtained in Step 1) as input for Kriging interpolation, a spatial covariance model is constructed by capturing the linear correlation of space to perform linear prediction of temperature and humidity at unmarked points. Step 3) Construct a multiple linear regression model with Kriging linear prediction, measured data at marked points, time dimension features, spatial features and external meteorological data as independent variables, and target temperature and humidity values ​​as dependent variables. Fit the Kriging prediction results in multiple dimensions, and generate the processed spatial prediction values ​​of temperature and humidity based on the fitted multiple linear regression model. Step 4) Perform residual fusion on the predicted values ​​after processing by the multiple linear regression model, and perform feature splicing with the measured temperature and humidity data of the marker points to construct a feature matrix. At the same time, based on the spatial location information of the marker points, obtain the geometric relationship and physical distance between each sensor node and construct an adjacency matrix. Step 5) Build a graph convolutional network model. Input the feature matrix and adjacency matrix from step 4) into the graph convolutional network model for training. Use the fitted prediction model to obtain the three-dimensional spatial point and surface distribution of indoor temperature and humidity in the study area.

2. The method for predicting indoor temperature and humidity spatial data by fusing spatial interpolation and graph convolutional networks according to claim 1, characterized in that, In step 1), the temperature and humidity data from each sensor are processed for missing values, data smoothing, noise reduction, and normalization. Specifically: For missing values ​​in the temperature and humidity data, a combination of interpolation and mean imputation is used to ensure data integrity; to eliminate noise in the data, exponential smoothing is used for data smoothing; since the fitting effect of the graph convolutional network is closely related to the data quality, the spatial location information and temperature and humidity data need to be normalized; the spatial coordinates of the marker points are scaled to the [0, 1] interval; at the same time, the temperature and humidity values ​​have large differences, so they need to be normalized to [0, 1] respectively to eliminate the difference in dimensions and ensure data consistency.

3. The method for predicting indoor temperature and humidity spatial data by fusing spatial interpolation and graph convolutional networks according to claim 1, characterized in that, In step 2), the semivariograms at different horizontal and vertical angles are calculated, and empirical semivariograms are plotted in the corresponding directions based on these semivariograms to capture the changes in spatial correlation with distance in different directions. Based on the variability of each direction in the semivariogram, the direction with stronger variability is determined as the main axis, and the direction with weaker variability is determined as the secondary axis. Then, a spatial covariance model is constructed based on the semivariogram model fitted by the Gaussian model, and the temperature and humidity of unmarked points are spatially predicted using the Kriging interpolation method.

4. The method for predicting indoor temperature and humidity spatial data by fusing spatial interpolation and graph convolutional networks according to claim 3, characterized in that, The specific steps are as follows: Calculate the Euclidean distance between each pair of marked points, and obtain the point pair (x... i x j Spatial distance h i Then, the point pairs are grouped according to the horizontal and vertical directions, and the point pairs (x) in different directions are calculated separately. i x j The interpolation square of the temperature and humidity values ​​[z(x)] i )-z(x j )] 2 , where z(x) is the temperature or humidity value of the marker point x; For a given distance h, calculate the squared mean of the differences between all pairs of points at distance h, and use this to calculate the semivariogram, as shown in the following formula: Wherein, γ(h k ) is a distance of h k The semivariogram values ​​between point pairs, N(h) k ) is a distance of h k The number of point pairs; Based on the calculated semivariogram values, an empirical semivariogram is plotted for each direction, and a Gaussian model is used for fitting. By comparing the variability in each direction, the principal axis and secondary axis are determined. Finally, using the fitted semivariogram, a spatial covariance model is defined, which reflects the following: For the target unmarked point, calculate its covariance with all known marked points, and construct a covariance vector; The target region marker P is calculated using the fitted semivariogram γ(h) and covariance function Cov(h). a With unmarked point P u The covariance values ​​are used to form a covariance vector. By solving the linear system Cw=C u Calculate the Kriging weights w to obtain the weights w of each known point to the unlabeled points. i ; Ultimately, the Kriging equation was created. Obtain the linear prediction results of temperature and humidity for unmarked points in the indoor space, where Z(x) i (x) is a known point. i The temperature and humidity values, Z(x0) is the linear prediction result of temperature and humidity without x0 label, w i To assign x to each group i For x u The weighting coefficients.

5. The method for predicting indoor temperature and humidity spatial data by fusing spatial interpolation and graph convolutional networks according to claim 1, characterized in that, In step 5), the feature matrix and adjacency matrix obtained in step 4) are input into the graph convolutional network model for training. and adjacency matrix As input to the Graph Convolutional Network (GCN), to ensure that the sensor nodes' own features participate in the convolution, the adjacency matrix is ​​used. Adding it to the self-loop identity matrix I yields the adjacency matrix with self-loops. Based on the degree of each sensor node Construct degree matrix And perform symmetric normalization to obtain For each layer l, through To achieve feature aggregation, where W (l) It is the weight matrix, which introduces the nonlinearity of the model through the nonlinear activation function σ = max(0, x), where x represents the result of the features of the l-th layer node after linear transformation and neighborhood aggregation; Optimization is performed by defining the mean squared error as the loss function, with the following formula: The gradient descent algorithm is used to minimize the loss, the network weights are updated, and the feature matrix G of the final output layer is obtained after multiple layers of graph convolution. (L) Represents the predicted temperature and humidity values ​​for each unlabeled node.

6. The method for predicting indoor temperature and humidity spatial data by fusing spatial interpolation and graph convolutional networks according to claim 1 or 5, characterized in that, In step 5), the fitted prediction model is used to obtain the three-dimensional spatial point-area distribution of indoor temperature and humidity in the study area, as follows: The distribution of three-dimensional target point data is presented in the form of three-dimensional scattered points. The three-dimensional mapping position of each target point in the real-world three-dimensional model is determined according to the three-dimensional coordinates (x, y, z). The temperature or humidity of the target point is mapped to a color through a color mapping function to show the data level. The 3D target surface data distribution uses spatial slicing to predict temperature and humidity values. The system renders and displays the spatial distribution of indoor temperature and humidity. The study area is divided into multiple xy-planes to construct multiple layers, with each layer generating a corresponding 3D model of the study area's x and y ranges using a lookup table function. Apply gradient color mapping Mapping to the corresponding color parameters yields the distribution of three-dimensional surface data of the indoor space.

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