A method and system for interpolating and predicting missing road environment data

Abstract

This invention proposes a method and system for interpolating and predicting missing road environment data, relating to the field of missing data imputation. The method includes: acquiring road environment sample data, preprocessing it, and removing seasonal factors; using the deseasoned road environment sample data as observations, inputting it into a multiple linear regression model for fitting, obtaining trend terms and residual terms; performing quadratic exponential smoothing on the residual terms, inputting the smoothed residual terms into a first-class product-sum model to calculate the spatiotemporal variability function, and fitting a spatiotemporal kriging model based on the spatiotemporal variability function; and using the spatiotemporal kriging model to estimate the data to be imputed, obtaining the interpolation prediction result. This invention first separates the residual terms through a multiple linear regression model, uses quadratic exponential smoothing to reduce residual noise, and then constructs a spatiotemporal variability function based on a first-class product-sum model to consider spatiotemporal interactions, which can quickly impute missing time series data of the road environment, thereby obtaining more accurate road environment data.

Description

Technical Field

[0001] This invention relates to the field of missing data completion technology, and in particular to a method and system for interpolating and predicting missing data in road environment. Background Technology

[0002] The collection and processing of road environment data (such as temperature, humidity, wind speed, and total radiation) is crucial for road environment monitoring, and complete road environment data is essential for understanding road dynamics. However, due to the complexity of the road operating environment, unstable communication quality, weather changes, and equipment failures, the road environment data collected in the actual environment may be missing or erroneous. Directly deleting missing or erroneous data will severely affect the sample distribution, hindering downstream tasks and ultimately impacting the final results. Therefore, appropriately supplementing and correcting these missing and erroneous data becomes critical to this research.

[0003] Interpolation methods are commonly used to complete and repair missing data. However, existing interpolation methods are not suitable for road environment data that simultaneously possesses temporal and spatial characteristics. For example, ordinary kriging interpolation cannot effectively identify the temporal characteristics of road environment data, making it difficult to accurately model the time dimension. While traditional spatiotemporal kriging interpolation considers spatiotemporal factors, its accuracy is still significantly insufficient when applied to road environment data, failing to meet practical needs. Furthermore, existing technologies have shortcomings in residual data processing, failing to conduct in-depth exploration and processing of residual data. Noise components in residual data can adversely affect missing value imputation, which is one of the key factors contributing to the poor performance of existing interpolation methods.

[0004] Furthermore, the challenge in restoring road environment data lies in time series imputation. Due to the instability of road environment data, the collected data is prone to large-scale, continuous gaps, including both time series data and the missing road environment data itself. To fill in the missing data, it is often necessary to impute the missing time series data during data preprocessing. For missing road environment data, preliminary interpolation methods can be used; however, for time series data, missing data often means that the evolution of the data over a period of time is unclear, and simple interpolation methods such as manual imputation are difficult to achieve fast and effective interpolation imputation. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a method and system for interpolating and predicting missing road environment data. It applies a spatiotemporal kriging model based on multiple linear regression to road environment data restoration. First, the residual terms of the original data are separated. Then, quadratic exponential smoothing is used to reduce residual noise. Next, a spatiotemporal variogram is constructed based on a first-class product-sum model, and the spatiotemporal kriging model is fitted to estimate missing values. This achieves accurate and efficient interpolation of data with temporal and spatial characteristics, thereby obtaining more accurate road environment data.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a method for interpolating and predicting missing road environment data, comprising:

[0008] Obtain road environment sample data, perform preprocessing and remove seasonal factors;

[0009] Seasonal road environment sample data were used as observations and input into a multiple linear regression model for fitting to obtain trend terms and residual terms.

[0010] The residual term is subjected to quadratic exponential smoothing. The smoothed residual term is then input into a first-class product summation model to calculate the spatiotemporal variability function. Finally, a spatiotemporal kriging model is fitted based on the spatiotemporal variability function.

[0011] The spatiotemporal kriging model is used to estimate the data to be filled, and the interpolation prediction results are obtained.

[0012] Preferably, the preprocessing includes: performing uniform format processing on the road environment sample data and deleting outliers based on the calibration range.

[0013] Preferably, the removal of seasonal factors specifically involves using an additive model in the time-series decomposition method to remove seasonal factors from the road environment sample data.

[0014] Preferably, the step of using deseasonalized road environment sample data as observations and inputting them into a multiple linear regression model for fitting to obtain trend terms and residual terms specifically includes:

[0015] The observed values ​​are input into a multiple linear regression model for fitting, and the trend term is estimated; the trend term is:

[0016] m(s,t)=β0+β1f1(s,t)+β2f2(s,t)+…+β p f p (s,t)

[0017] Among them, f i (s,t) represents the independent variable, β i Represents the regression coefficient;

[0018] Subtracting the estimated trend term from the observed values ​​yields the residual term; the residual term ε(s,t) is:

[0019] ε(s,t)=Z(s,t)-m(s,t)

[0020] Where Z(s,t) represents the observed value, m(s,t) represents the trend term, s represents the spatial location, and t represents time. Preferably, the quadratic exponential smoothing of the residual term specifically includes:

[0021] Y t+h =L t +hT t

[0022] L t =αY t +(1-α)(L t-1 +T t-1 )

[0023] T t =β(L t -L t-1 )+(1-β)T t-1

[0024] Among them, Y t+h L represents the smoothed residual term, which is the predicted value of the residual term at time t+h; t For the estimation of the level component at time t, T t Estimate the trend component at time t; Y t L is the actual observed value of the residual term at time t; α is the horizontal smoothing constant used to control the response to the current observed value of the residual term; t-1 It is the level component estimate at time t-1; T t-1 is the trend component estimate at time t-1; β is the trend smoothing constant used to control the trend response; L t -L t-1 This represents the change in the horizontal component estimate between the current time t and time t-1, reflecting the change in the horizontal trend.

[0025] Preferably, the step of inputting the smoothed residual term into a type of product-sum model to calculate the spatiotemporal variability function specifically includes:

[0026] γ st (h,τ)=[k1C t (0)+k2]γ(h)+[k1C s (0)+k3]γ(τ)-k1γ(h)γ(τ)

[0027]

[0028] Where, γ st (h,τ), γ(h), and γ(τ) are the spatiotemporal variogram, spatial variogram, and temporal variogram, respectively; C t (0), C s (0) represents the sill values ​​corresponding to the time variability function and the spatial variability function; N(h) represents the number of observation pairs at a distance of h; Z(x) represents the number of observation pairs at a distance of h. i ) is at position x i The observed values; h is the spatial distance; N(τ) is the number of observation pairs with a time interval of τ; Z(t) i ) represents the time point t i The observed values; τ is the time interval, and k1, k2, and k3 are model parameters.

[0029] Preferably, the step of estimating the data to be filled using the spatiotemporal kriging model to obtain the interpolation prediction result specifically includes:

[0030]

[0031] Wherein, ε(s) i ,t i ) represents the residual term of the data to be filled. To estimate the obtained residual term, λ i The spatiotemporal kriging weights are obtained from the kriging system equations; the kriging system equations are:

[0032]

[0033] Where, γ((s) i ,t i ),(s j ,t j The spatiotemporal variogram, determined by a type of product-sum model, is the value at a spatiotemporal point (s). i ,t i ) and (s j ,t j The variation values ​​between )

[0034] The trend term m(s,t) of the data to be filled and the estimated residual term Seasonal component S t Combined with the noise d removed by quadratic exponential smoothing, the restored road environment data is obtained:

[0035]

[0036] d = Y t+h -Y t

[0037] Among them, Y t+hY is the smoothed residual term. t These are the residual data before smoothing.

[0038] Secondly, the present invention provides a road environment missing data interpolation prediction system, comprising:

[0039] The data acquisition module is used to acquire road environment sample data, perform preprocessing, and remove seasonal factors;

[0040] The regression fitting module is used to take deseasonalized road environment sample data as observations, input them into a multiple linear regression model for fitting, and obtain the trend term and residual term.

[0041] The function and model building module is used to perform quadratic exponential smoothing on the residual term, input the smoothed residual term into a first-class product summation model to calculate the spatiotemporal variability function, and fit a spatiotemporal kriging model based on the spatiotemporal variability function.

[0042] The interpolation prediction module is used to estimate the data to be filled using the spatiotemporal kriging model to obtain the interpolation prediction result.

[0043] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the road environment missing data interpolation prediction method described in the first aspect.

[0044] Fourthly, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the road environment missing data interpolation prediction method described in the first aspect.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] (1) This invention applies the spatiotemporal regression Kriging model to the scenario of repairing missing road environment data. By first using a multiple linear regression model to capture the overall trend of the data, the trend term and residual term are effectively separated. On this basis, the residual term is subjected to quadratic exponential smoothing to remove noise, and then a spatiotemporal variability function is constructed based on a first-class product summation model. This model can fully consider the interaction between time and space, and can better capture the continuous changes in environmental factors such as temperature in time and their spatial correlation for time series data in the road environment, thereby effectively and quickly filling in the missing data.

[0047] (2) This invention uses a spatiotemporal kriging model to perform fine estimation of the spatiotemporal characteristics of the residual term. This process makes full use of the spatiotemporal correlation of the data. The spatiotemporal correlation information provided by the spatiotemporal variogram based on a type of product summation model helps to improve the accuracy of the model when filling in the data, reduce the filling error, and thus improve the accuracy of the prediction of missing data.

[0048] (3) In addition, the format standardization and outlier handling in the preprocessing steps ensured the quality of the input data, laying a solid foundation for subsequent model fitting. This invention not only solves the problem of missing road environment data due to various reasons, but also enhances the spatiotemporal coherence of the data, providing more reliable data support for the monitoring, analysis and management of the road environment.

[0049] (4) Since the residuals calculated using multiple linear regression are noisy, this invention uses quadratic exponential smoothing to reduce the noise in the residuals and make the data meet the stationarity condition. Because this invention uses time series decomposition in the early stage, that is, it effectively removes the seasonal factors in the residuals through time series decomposition, this invention chooses quadratic exponential smoothing, which is more suitable for data with trends but no seasonality, compared with the conventional exponential smoothing method, and can further extract the time trend in the data.

[0050] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0051] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute a limitation thereof.

[0052] Figure 1 A flowchart illustrating the main steps of a road environment missing data interpolation prediction method provided in this embodiment of the invention;

[0053] Figure 2 This is a schematic diagram illustrating the de-seasonalization data comparison of a site provided in an embodiment of the present invention;

[0054] Figure 3 An autocorrelation graph of a site provided in an embodiment of the present invention;

[0055] Figure 4 This is a schematic diagram comparing residual data before and after quadratic exponential smoothing, provided in an embodiment of the present invention.

[0056] Figure 5 This is a schematic diagram of spatial variogram fitting provided in an embodiment of the present invention;

[0057] Figure 6 This is a schematic diagram of fitting the ideal spatial variogram function according to an embodiment of the present invention;

[0058] Figure 7 A schematic diagram of time variation function fitting provided in an embodiment of the present invention;

[0059] Figure 8 This is a schematic diagram of fitting an ideal time variation function according to an embodiment of the present invention;

[0060] Figure 9 A three-dimensional image of an ideal spatiotemporal variability function provided for an embodiment of the present invention. Detailed Implementation

[0061] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0062] Example 1

[0063] like Figure 1 As shown in the figure, this embodiment discloses a method for interpolating and predicting missing road environment data, including the following steps:

[0064] S1: Obtain road environment sample data, perform preprocessing and remove seasonal factors;

[0065] S2: Use seasonal road environment sample data as observations, input them into a multiple linear regression model for fitting, and obtain the trend term and residual term;

[0066] S3: Perform a second exponential smoothing on the residual term, input the smoothed residual term into a first-class product summation model to calculate the spatiotemporal variability function, and fit a spatiotemporal kriging model based on the spatiotemporal variability function.

[0067] S4: The spatiotemporal kriging model is used to estimate the data to be filled, and the interpolation prediction result is obtained.

[0068] Next, combined Figure 1 This embodiment provides a detailed description of a method for interpolating and predicting missing road environment data. In this method, a spatiotemporal kriging model is first constructed based on training data, and then the constructed spatiotemporal kriging model is used for interpolating and predicting missing data in the actual road environment.

[0069] (I) Data Preparation and Preprocessing

[0070] 1. Collect road environment data, process the data to ensure that the data format is consistent, and the format includes time, spatial coordinates (latitude and longitude) and measurement values.

[0071] 2. Based on road environment data in a unified format, visualization processing can be performed. Data distribution, trends, and periodicity can be obtained by drawing scatter plots, time series plots, etc.

[0072] It should be noted that data visualization, such as drawing scatter plots and time series plots, are all conventional techniques well-known to those skilled in the art, and their specific implementation methods will not be elaborated here.

[0073] 3. Perform data preprocessing based on the data's distribution, trends, and periodicity.

[0074] If outliers are found (for example, data points that deviate significantly from the area where most data points are located in a scatter plot or other visualization), the outliers are removed.

[0075] If an overall trend emerges, detrending can be used. For example, when studying the impact of vegetation cover changes on humidity within a road area, if the humidity data itself shows an increasing trend year by year due to climate change, directly building a model might attribute this trend to the influence of vegetation cover changes, when in reality this influence is caused by other macroeconomic factors. Detrending (using methods such as differencing and decomposition) can separate this trend factor, allowing the model to focus more on studying the true relationship between variables.

[0076] If periodicity is observed, a suitable spatiotemporal model can be constructed to extract the periodic characteristics. For example, for road traffic flow data, if daily or weekly periods are present, a corresponding daily or weekly spatiotemporal model can be constructed to more accurately predict traffic flow. By capturing this potential pattern of periodicity, a reference basis can be provided for subsequent data supplementation.

[0077] 4. Since the training of the spatiotemporal regression model required in this embodiment requires a complete dataset, it is necessary to initially identify missing values ​​and impute them using simple interpolation or neighboring values. This will make the dataset formally complete, enabling the initial training and parameter estimation of spatiotemporal regression models and other methods, thus ensuring the smooth modeling of the subsequent spatiotemporal kriging model.

[0078] After the above data preparation and preprocessing steps, we obtained data that meets the requirements. Next, we will build a regression model based on this data.

[0079] 5. Using the additive model in time series decomposition, seasonal factors are extracted from the preprocessed road environment sample data to remove seasonality. The formula for the additive model is:

[0080] Y t =T t +S t +R t

[0081] Among them, Y t These are observations in a time series; T tIt is a trend component; S t It is a seasonal component; R t It is a random component.

[0082] like Figure 2 This is a diagram illustrating the comparison of seasonal data from a single site (data collection location). After removing seasonal factors, the road environment sample data is as follows:

[0083] P t =T t +R t

[0084] Among them, P t To obtain seasonal road environment sample data, T t Trend component; R t It is a random component.

[0085] (II) Establishing a regression model and calculating the residuals

[0086] First, the trend term of the preprocessed data is fitted using a regression model, that is, the trend of the data changing with space and time is estimated by using linear regression or other regression models.

[0087] Specifically, given the observed value Z(s,t), it is decomposed into a trend term m(s,t) and a residual term ε(s,t):

[0088] Z(s,t)=m(s,t)+ε(s,t)

[0089] Where s represents spatial location and t represents time.

[0090] The trend term m(s,t) can be estimated using a regression model; in this embodiment, a multiple linear regression model is preferred.

[0091] m(s,t)=β0+β1f1(s,t)+β2f2(s,t)+…+β p f p (s,t)

[0092] Among them, f i (s,t) represents the independent variable, which can be selected from relevant variables such as time (different moments), spatial location (different places), and environmental factors (such as temperature, humidity, etc.); β i It is the regression coefficient.

[0093] In this embodiment, temperature observation data is selected as an example. For temperature observation data along a certain highway, s represents different locations on the highway (e.g., kilometers from the starting point), t represents different times of day (e.g., hourly), and f i (s,t) represents the temperature value at a certain location on the highway at a certain time, and β1 is the corresponding regression coefficient.

[0094] Subtracting the estimated trend term from the observed values ​​yields the residual ε(s,t):

[0095] ε(s,t)=Z(s,t)-m(s,t)

[0096] Where s represents spatial location and t represents time.

[0097] In this embodiment, a temperature monitoring point is set up every 10 kilometers along a certain highway section, and the temperature data is recorded once per hour as the observation value Z(s,t). The trend term m(s,t) corresponding to the location and time is calculated by the above-mentioned multiple linear regression model, and then the residual ε(s,t) is obtained by subtraction.

[0098] Furthermore, after obtaining the trend term and residual term, the residual term is analyzed. The residuals are evaluated to intuitively understand the degree of deviation between the model's predicted values ​​and the actual observed values, thereby determining the reliability of the model.

[0099] Specifically, the quality of the regression model is judged by calculating the autocorrelation of the residuals. For example... Figure 3 The autocorrelation plot of one of the sites shows that most of the data is within the confidence interval, and the data outside the confidence interval does not exceed 0.25. This proves that the regression model has good fit and stability.

[0100] Subsequently, in order to obtain a smoother residual sequence that better reflects the inherent regularity of the residual term and has less noise influence, a second exponential smoothing is performed on the residual term. Its basic formula is mainly divided into two parts: level component and trend component.

[0101] First, regarding the horizontal components:

[0102] L t =αY t +(1-α)(L t-1 +T t-1 )

[0103] Among them, L t Estimate the level component at time t; Y t L is the actual observed value of the residual term at time t; α is the horizontal smoothing constant used to control the response to the current observed value of the residual term; t-1 It is the level component estimate at time t-1; T t-1 It is the trend component estimate at time t-1.

[0104] Secondly, regarding trend components:

[0105] T t =β(L t -L t-1)+(1-β)T t-1

[0106] Among them, T t This estimates the trend component at time t; β is the trend smoothing constant used to control the trend response; L t -L t-1 This represents the change in the horizontal component estimate between the current time t and time t-1, reflecting the change in the horizontal trend.

[0107] The smoothed residual term is then expressed as:

[0108] Y t+h =L t +hT t

[0109] Among them, Y t+h The term is the smoothed residual, and the predicted value of the residual at time t+h.

[0110] The noise d removed by quadratic exponential smoothing is expressed as:

[0111] d = Y t+h -Y t

[0112] Among them, Y t These are the residual data before smoothing.

[0113] Finally, the standard deviation was used to evaluate the random noise results, and the results are shown in Table 1:

[0114] Table 1. Comparison of standard deviations of the original data and the data after quadratic exponential smoothing.

[0115]

[0116] Combination Figure 4 The diagram showing the comparison of residual data before and after quadratic exponential smoothing clearly demonstrates that the residual noise is significantly reduced after quadratic exponential smoothing.

[0117] This embodiment employs quadratic exponential smoothing, which can reduce the impact of random noise in the residuals by smoothing historical data, making the potential patterns in the residuals clearer. Furthermore, quadratic exponential smoothing is computationally simple and suitable for processing large-scale spatiotemporal data, especially when rapid model updates are required. It can efficiently handle residuals, effectively improving computational efficiency and prediction accuracy while maintaining model flexibility.

[0118] (III) Selection of the Spatiotemporal Variation Function

[0119] First, time variograms and spatial variograms are constructed based on the residuals, and the temporal and spatial correlations of the residuals are verified by plotting the corresponding variograms.

[0120] Specifically, a spatial variogram is constructed based on the residuals. The formula for the spatial variogram is as follows:

[0121]

[0122] Where γ(h) is the spatial variability function; N(h) is the number of observation pairs at a distance of h; Z(x) i ) is at position x i The observed value; h is the spatial distance.

[0123] Based on the spatial variability function, plot as follows: Figure 5 The spatial variogram shown is compared with... Figure 6 Compare the images fitted with the ideal spatial variogram, if... Figure 5 and Figure 6 The matching curves indicate that the residuals have spatial correlation.

[0124] The time variability function is constructed based on the residuals. The formula for the time variability function is as follows:

[0125]

[0126] Where γ(τ) is the time variation function; N(τ) is the number of observation pairs with a time interval of τ; Z(t) i ) represents the time point t i The observed value; τ is the time interval.

[0127] Based on the time variation function, plot as follows: Figure 7 The time variation function graph shown is consistent with... Figure 6 Compare the images fitted with the ideal time variation function, if... Figure 7 and Figure 8 The matching curves indicate that the residuals have a time correlation.

[0128] It should be understood that when the distribution of data points in the variogram plotted based on the residuals can closely approximate (within a reasonable error range) the ideal variogram plot, Figure 6 or Figure 8 When the data points and the ideal spatial variogram curve are closely related, they can be considered to be "matched". For example, in a spatial variogram, if most data points fall around the ideal spatial variogram curve and the distance between these points and the curve is small (this can be determined by setting a reasonable error threshold, such as the root mean square error being less than a certain value), then the two are considered to be matched. Similarly, for a time variogram, if the data points and the ideal time variogram curve show a similar degree of closeness at the corresponding time intervals, they can also be considered to be matched.

[0129] Once the spatiotemporal correlation of the residuals is determined through comparison of the aforementioned variogram plots, a spatiotemporal variogram is constructed based on these spatiotemporally correlated residuals. By quantifying this correlation and expressing it in functional form, the evolution of data in the spatiotemporal domain can be further explored, enabling more effective use of this information in subsequent data analysis, prediction, or other related research.

[0130] The spatiotemporal variability function is commonly used to describe the variability between the spatial and temporal separation of two points and their observed values. Its basic formula is as follows:

[0131]

[0132] Where γ(h,τ) is the spatiotemporal variability function, N(h,τ) is the number of observation pairs with a time interval of τ and a spatial interval of h, and Z(x) is the number of observation pairs with a time interval of τ and a spatial interval of h. i ,t i At time point t i and spatial point x i The observed values.

[0133] Research on spatiotemporal variogram models mainly falls into two categories: separable models and non-separable models.

[0134] Separable models are relatively simple, with common ones including spherical models, exponential models, or Gaussian models. They are mainly obtained by combining time variograms and spatial variograms in the form of addition or multiplication, but they cannot well express the relevant information of time and space.

[0135] While the construction process of inseparable models is relatively complex, they can more effectively represent the correlation between variables in time and space. Among them, a type of product-sum model is a commonly used inseparable model, represented as follows:

[0136] γ st (h s ,h t )=[(k1C t (0)+k2]γ s (h s )+[k1C s (0)+k3]γ t (h t )-k1γ s (h s )γ t (h t )

[0137] Where, γ st (h s ,h t ), γ s (h s ) and γt (h t ) represents the spatiotemporal variogram, spatial variogram, and temporal variogram; C t (0), C s (0) represents the sill values ​​corresponding to the temporal and spatial variograms. These spatiotemporal variograms provide information about the spatiotemporal correlation structure of the data. This correlation structure is used to determine the kriging weights when constructing the spatiotemporal kriging model.

[0138] A three-dimensional variogram was plotted on the spatiotemporal variogram constructed based on a type of product-sum model, and compared with... Figure 9 If the shape and trend of the three-dimensional variogram match the pattern expected by the ideal spatiotemporal variogram, it indicates that the constructed spatiotemporal variogram can reasonably reflect the correlation of data in time and space.

[0139] Calculate evaluation metrics (such as MAE, RMSE, etc.), check the goodness of fit of the results, and use R... 2 The adaptability of the model is evaluated using indicators such as AIC or BIC, and the rationality and accuracy of the spatiotemporal variability function constructed based on a type of product summation model are verified. It should be understood that the relevant verification methods are achievable by those skilled in the art.

[0140] In this embodiment, a product-sum model can fully consider the interaction between time and space. For time-series data in the road environment, this model can better capture the continuous temporal changes and spatial correlations of environmental factors such as temperature. Once the model is trained, the interpolation method based on the spatiotemporal variogram can be quickly applied to missing data points because the model has quantified the spatiotemporal correlations and can directly infer the values ​​of missing data based on the information of known data points.

[0141] Because a certain type of product-based model can effectively handle spatiotemporal correlations, it can more accurately describe the changing patterns of road environment data compared to simple separable models. As shown in Table 2, by calculating evaluation indicators such as MAE and RMSE, compared with other models, the product-based model has an RMSD of 0.0101. A low RMSD value means that the average deviation between the predicted and actual values ​​is extremely small, almost negligible, and can accurately approximate the actual observation data. The MAE is 8.04, indicating that the model exhibits extremely high accuracy in fitting road environment data. Therefore, the spatiotemporal variogram based on the product-based model can provide more accurate results when filling in data, reducing filling errors and thus better reflecting the true state of the road environment.

[0142] Table 2 Performance Comparison of Different Models

[0143]

[0144] The spatiotemporal variogram, constructed based on a type of product-sum model, has already been able to capture the temporal and spatial correlations of data quite well. However, in order to accurately interpolate and predict missing data in the road domain environment, it is necessary to further utilize these spatiotemporal variograms to construct a spatiotemporal kriging model.

[0145] (iv) Real-time interpolation of spatiotemporal kriging models

[0146] Spatiotemporal kriging models rely on accurate spatiotemporal variability functions for prediction and interpolation.

[0147] 1. Data identification and data processing

[0148] First, missing and outlier values ​​in the real-time data to be filled are identified. For temperature data in a road environment, assuming multiple temperature monitoring points are set up along a highway to collect temperature data at different times and locations, missing values ​​can be temporarily interpolated directly. However, outliers that are outside the calibration range need to be deleted first, and then temporary interpolation is performed to obtain a complete dataset without missing or outlier values.

[0149] Then, based on the above dataset, the trend term m(s,t) for the missing region is calculated using a multiple linear regression model.

[0150] 2. Spatiotemporal Kriging Estimation

[0151] After calculating the trend term m(s,t) for the missing region, spatiotemporal kriging estimation is performed on the residuals of the missing region based on the pre-constructed spatiotemporal regression kriging model. That is, given the spatial and temporal points (s0,t0) of the missing region, the residual values ​​are estimated using the kriging method. The announcement is as follows:

[0152]

[0153] Where, λ i The spatiotemporal kriging weights are obtained from the kriging system equations. The kriging system equations are:

[0154]

[0155] Where, γ((s) i ,t i ),(s j ,t j The spatiotemporal variogram, determined by a type of product-sum model, is the value at a spatiotemporal point (s). i ,t i ) and (s j ,t jThe variation between these two points, for temperature data, reflects the strength of the correlation between the data at these two spatiotemporal points, and is thus used to calculate the spatiotemporal kriging weight λ. i .

[0156] 3. Combined Prediction Results

[0157] The estimated trend term m(s,t) and the residual term estimated by spatiotemporal kriging are combined. Combination, seasonal components S t The noise d, which has been smoothed by quadratic exponential smoothing, is added to obtain the final Kriging interpolation of the road environment data at the missing locations. This predicted value is highly accurate and can effectively repair missing locations. The specific formula is as follows:

[0158]

[0159] In this specific embodiment, the application of spatiotemporal regression kriging is mainly reflected in repairing missing road environment data and improving prediction accuracy. Initial time series decomposition removes seasonal factors, and then multiple linear regression is used to capture the overall trend and separate residual terms. Quadratic exponential smoothing is applied to the residual terms to reduce noise and further extract time trends, enhancing the accuracy of data filling. Subsequently, a spatiotemporal variogram based on a first-class product-sum model is used to fully consider the spatiotemporal interaction and better capture data characteristics. Through regression analysis, the relationship between time, space, and road environment data can be established, allowing the prediction of missing and erroneous data values ​​using existing time and space data. Furthermore, when processing the collected data, the data is first preprocessed, then a regression model is applied to capture trends and calculate residuals. Spatiotemporal kriging is then used to interpolate these residuals, thereby obtaining more accurate road environment data. This method not only reduces the uncertainty caused by missing data but also improves the overall assessment of the road environment.

[0160] Example 2

[0161] This embodiment provides a road environment missing data interpolation prediction system, including:

[0162] The data acquisition module is used to acquire road environment sample data, perform preprocessing, and remove seasonal factors;

[0163] The regression fitting module is used to take deseasonalized road environment sample data as observations, input them into a multiple linear regression model for fitting, and obtain the trend term and residual term.

[0164] The function and model building module is used to perform quadratic exponential smoothing on the residual term, input the smoothed residual term into a first-class product summation model to calculate the spatiotemporal variability function, and fit a spatiotemporal kriging model based on the spatiotemporal variability function.

[0165] The interpolation prediction module is used to estimate the data to be filled using the spatiotemporal kriging model to obtain the interpolation prediction result.

[0166] Example 3

[0167] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the road environment missing data interpolation prediction method described in Embodiment 1 above.

[0168] Example 4

[0169] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the road environment missing data interpolation prediction method described in Embodiment 1 above.

[0170] The steps or modules involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0171] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for interpolating and predicting missing road environment data, characterized in that, include: Obtain road environment sample data, perform preprocessing and remove seasonal factors; Seasonal road environment sample data were used as observations and input into a multiple linear regression model for fitting to obtain trend terms and residual terms. The residual term is subjected to quadratic exponential smoothing. The smoothed residual term is then input into a first-class product summation model to calculate the spatiotemporal variability function. Finally, a spatiotemporal kriging model is fitted based on the spatiotemporal variability function. The spatiotemporal kriging model is used to estimate the data to be filled, and the interpolation prediction results are obtained, specifically including: in, For the residual terms of the data to be filled, To estimate the obtained residual term, The spatiotemporal kriging weights are obtained from the kriging system equations; the kriging system equations are: in, It is determined by the spatiotemporal variogram constructed based on a type of product-sum model at a specific point in time. and The variation values ​​between; Trend items of the data to be filled Estimated residuals Seasonal ingredients Noise removed with quadratic exponential smoothing Combined, the repaired road environment data is obtained: in, The smoothed residual term, These are the residual data before smoothing.

2. The method for interpolating and predicting missing road environment data as described in claim 1, characterized in that, The preprocessing includes: performing uniform format processing on the road environment sample data and deleting outliers based on the calibration range.

3. The method for interpolating and predicting missing road environment data as described in claim 1, characterized in that, The removal of seasonal factors specifically involves using an additive model in the time-series decomposition method to remove seasonal factors from the road environment sample data.

4. The method for interpolating and predicting missing road environment data as described in claim 1, characterized in that, The process involves using deseasonalized road environment sample data as observations, inputting them into a multiple linear regression model for fitting, and obtaining trend and residual terms, specifically including: The observed values ​​are input into a multiple linear regression model for fitting, and the trend term is estimated; the trend term is: in, Indicates the independent variable. Represents the regression coefficient; The residual term is obtained by subtracting the estimated trend term from the observed values; the residual term for: in, Represents the observed value. Indicates the trend term. s Indicates spatial location, t Indicates time.

5. The method for interpolating and predicting missing road environment data as described in claim 1, characterized in that, The process of performing quadratic exponential smoothing on the residual term specifically includes: in, The smoothed residual term is the predicted value of the residual term at time t+h; Estimate the level component at time t. Estimate the trend component at time t; It is the actual observed value of the residual term at time t; It is a horizontal smoothing constant used to control the response to the current residual term observations; It is the level component estimate at time t-1; It is an estimate of the trend component at time t-1; It is a trend smoothing constant used to control the response to trends; This represents the change in the horizontal component estimate between the current time t and time t-1, reflecting the change in the horizontal trend.

6. The method for interpolating and predicting missing road environment data as described in claim 1, characterized in that, The step of inputting the smoothed residual term into a type of product-sum model to calculate the spatiotemporal variability function specifically includes: in, , and These are the spatiotemporal variogram, the spatial variogram, and the temporal variogram, respectively. , These are the sill values ​​corresponding to the time variogram and the space variogram; Let h be the number of observation pairs at a distance of h; For the position is The observed value; h is the spatial distance; The time interval is The number of observation pairs; For at a certain point in time Observed values; For time intervals, These are the model parameters.

7. A road environment missing data interpolation prediction system, based on the road environment missing data interpolation prediction method as described in claim 1, characterized in that, include: The data acquisition module is used to acquire road environment sample data, perform preprocessing, and remove seasonal factors; The regression fitting module is used to take deseasonalized road environment sample data as observations, input them into a multiple linear regression model for fitting, and obtain the trend term and residual term. The function and model building module is used to perform quadratic exponential smoothing on the residual term, input the smoothed residual term into a first-class product summation model to calculate the spatiotemporal variability function, and fit a spatiotemporal kriging model based on the spatiotemporal variability function. The interpolation prediction module is used to estimate the data to be filled using the spatiotemporal kriging model to obtain the interpolation prediction result.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the road environment missing data interpolation prediction method as described in any one of claims 1-6.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the road environment missing data interpolation prediction method as described in any one of claims 1-6.

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