Road domain environment missing data interpolation prediction method and system

Abstract

The invention provides a road domain environment missing data interpolation prediction method and system, and relates to the field of missing data filling. The method comprises the following steps: acquiring road domain environment sample data, preprocessing and removing seasonal factors; inputting the de-seasonal road domain environment sample data as observation values into a multiple linear regression model for fitting to obtain a trend term and a residual term; performing secondary exponential smoothing on the residual term, inputting the smoothed residual term into a one-class product sum model to calculate a space-time variation function, and fitting a space-time Kriging model according to the space-time variation function; and estimating the to-be-filled data by using the space-time Kriging model to obtain an interpolation prediction result. According to the method, the residual term is separated through the multiple linear regression model, the residual noise is reduced by using the secondary exponential smoothing, and the space-time variation function is constructed based on the one-class product sum model to consider the space-time interaction, so that the missing of the road domain environment time sequence data can be quickly filled, and the more accurate road domain environment data can be obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of missing data filling, and in particular to a method and system for interpolating and predicting missing data in a road environment. Background Art

[0002] The collection and processing of road environment data (such as temperature, humidity, wind speed, total radiation, etc.) is the key to road environment monitoring. Complete road environment data is necessary to grasp the dynamics of the road. However, due to the complex road operation environment, unstable communication quality, weather changes, equipment failures and other issues, the road environment data collected in the actual environment may be missing or erroneous. For missing or erroneous data, if it is directly deleted, it will seriously affect the sample distribution, resulting in the inability to smoothly carry out downstream tasks, and thus affecting the final results. Therefore, the corresponding completion and repair of these missing and erroneous data has become the key to the research.

[0003] Interpolation methods are often used to complete missing data, but existing interpolation methods are not suitable for road environment data that has both temporal and spatial characteristics. For example, when processing road environment data, ordinary Kriging interpolation methods cannot effectively identify the temporal characteristics of the data, making it difficult to accurately model the time dimension; and although the traditional spatiotemporal Kriging interpolation method takes into account temporal and spatial factors, when applied to road environment data, its accuracy is still significantly insufficient and cannot meet actual needs. At the same time, existing technologies have deficiencies in residual data processing, and have failed to conduct in-depth research and processing of residual data. The noise components in the residual data will have an adverse effect on the filling of missing values, which is one of the key factors that lead to the poor results of existing interpolation methods.

[0004] In addition, the difficulty in repairing road environment data lies in filling in the time series. Due to the instability of road environment data, the collected data is prone to large-scale continuous missing of time series and road environment data itself. In order to complete the missing data, it is often necessary to fill in the missing time series during data preprocessing. For missing road environment data, preliminary interpolation methods can be used for interpolation; but for time series, missing often means that the evolution process of data over a period of time is unclear. It is difficult to achieve fast and effective interpolation filling using simple interpolation methods such as manual filling. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a method and system for interpolation prediction of missing data of road environment, and applies the spatiotemporal Kriging model of multivariate linear regression to road environment data restoration. The residual terms of the original data are first separated, and then the residual noise is reduced by quadratic exponential smoothing. After that, the spatiotemporal variation function is constructed based on a type of product-sum model and the spatiotemporal Kriging model is fitted to estimate the missing values, so as to achieve accurate and efficient interpolation of data with time and space characteristics, thereby obtaining more accurate road environment data.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

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

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

[0009] The deseasonalized road environment sample data are used as observation values ​​and input into the multivariate linear regression model for fitting to obtain the trend term and residual term.

[0010] Performing quadratic exponential smoothing on the residual term, inputting the smoothed residual term into a type of product-sum model to calculate the spatiotemporal variogram, and fitting the spatiotemporal Kriging model according to the spatiotemporal variogram;

[0011] The space-time Kriging model is used to estimate the data to be filled and obtain the interpolation prediction result.

[0012] Preferably, the preprocessing includes: performing unified format processing on the road environment sample data and deleting abnormal values ​​based on a calibration range.

[0013] Preferably, the removing of seasonal factors specifically includes: using an additive model in a time series decomposition method to remove seasonal factors in the road environment sample data.

[0014] Preferably, the deseasonalized road environment sample data is used as observation values ​​and input into a multiple linear regression model for fitting to obtain trend terms and residual terms, specifically including:

[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] The estimated trend term is subtracted from the observed value to obtain the residual term; the residual term ε(s, t) is:

[0019] ε(s,t)=Z(s,t)-m(s,t)

[0020] Wherein, Z(s, t) represents the observed value, m(s, t) represents the trend term, s represents the spatial position, and t represents the time. Preferably, performing secondary exponential smoothing on 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 is the smoothed residual term, which is the predicted value of the residual term at time t+h; L t is the horizontal component estimate at the current time t, T t Y is the trend component estimate at the current time t; t is the actual observed value of the residual term at the current time t; α is the horizontal smoothing constant, which is used to control the response to the current observed value of the residual term; L t-1 is the horizontal 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 It represents the change between the current time t and the time t-1 when the horizontal component is estimated, which is used to reflect the change of the horizontal trend.

[0025] Preferably, the step of inputting the smoothed residual term into a product-sum model to calculate the spatiotemporal variogram 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] Among them, 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) is the base value corresponding to the temporal variogram and spatial variogram; N(h) is the number of observation pairs with distance h; Z(x i ) is at position x i The observed value; h is the spatial distance; N(τ) is the number of observation pairs with a time interval of τ; Z(t i ) is the time point t i ; τ is the time interval, k1, k2, k3 are model parameters.

[0029] Preferably, the method of using the spatiotemporal Kriging model to estimate the data to be filled and obtain the interpolation prediction result specifically includes:

[0030]

[0031] Among them, ε(s i ,t i ) is the residual term of the data to be filled, is the estimated residual term, λ i is the spatiotemporal Kriging weight, obtained by the Kriging system equation; the Kriging system equation is:

[0032]

[0033] Among them, γ((s i ,t i ),(s j ,t j )) is a spatiotemporal variogram constructed based on a type of product-sum model and determined at a spatiotemporal point (s i ,t i ) and (s j ,t j ) between the values ​​of variation;

[0034] The trend term m(s, t) of the data to be filled and the estimated residual term Seasonal ingredients 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+his the residual term after smoothing, Y t is the residual data before smoothing.

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

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

[0040] The regression fitting module is used to take the deseasonalized road environment sample data as observation values, input them into the multivariate linear regression model for fitting, and obtain the trend term and residual term;

[0041] A function and model building module, for performing secondary exponential smoothing on the residual term, inputting the smoothed residual term into a type of product-sum model to calculate the spatiotemporal variogram, and fitting the spatiotemporal Kriging model according to the spatiotemporal variogram;

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

[0043] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a method for interpolating and predicting missing data in a road environment as described in the first aspect.

[0044] In a fourth aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in the method for interpolating and predicting missing data in a road environment described in the first aspect are implemented.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] (1) The present invention applies the spatiotemporal regression kriging model to the repair scenario of missing road environment data. The overall trend of the data is first captured by using a multivariate linear regression model, and the trend term and the residual term are effectively separated. On this basis, the residual term is subjected to secondary exponential smoothing to remove noise, and then the spatiotemporal variation function is constructed based on a type of product-sum model. The model can fully consider the interaction between time and space. For time series data in the road environment, it can better capture the continuous changes in time and spatial correlation of environmental factors such as temperature, and thus can effectively and quickly fill in the missing data.

[0047] (2) The present invention uses the spatiotemporal Kriging model to make a fine estimate 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 variation function constructed based on a type of product-sum model helps to improve the accuracy of the model when filling in data, reduce filling errors, and thus improve the accuracy of missing data prediction.

[0048] (3) In addition, the format unification and outlier processing in the preprocessing step ensure the quality of the input data and lay a solid foundation for subsequent model fitting. The present 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, in order to reduce the noise of the residuals and make the data meet the conditions of stationarity, the present invention uses the quadratic exponential smoothing method. Since the present invention used the time series decomposition method in the early stage, that is, the seasonal factors in the residuals were effectively removed by time series decomposition, compared with the conventional exponential smoothing method, the present invention selects the quadratic exponential smoothing method which is more suitable for data with trends but no seasonality, and can further extract the time trend in the data.

[0050] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their description are used to explain the present invention but do not constitute a limitation of the present invention.

[0052] Figure 1 A main flow chart of a method for interpolating and predicting missing data of a road environment provided by an embodiment of the present invention;

[0053] Figure 2 A schematic diagram of de-seasonalized data comparison of a site provided by an embodiment of the present invention;

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

[0055] Figure 4 A schematic diagram of the comparison of residual data before and after the second exponential smoothing provided by the embodiment of the present invention;

[0056] Figure 5 A schematic diagram of spatial variogram fitting provided by an embodiment of the present invention;

[0057] Figure 6 A schematic diagram of an ideal spatial variation function fitting provided by an embodiment of the present invention;

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

[0059] Figure 8 A schematic diagram of an ideal time variation function fitting provided by an embodiment of the present invention;

[0060] Fig. 9 A three-dimensional image of an ideal space-time variation function provided by an embodiment of the present invention. DETAILED DESCRIPTION

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

[0062] Embodiment 1

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

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

[0065] S2: The deseasonalized road environment sample data is used as observation values ​​and input into the multivariate linear regression model for fitting to obtain the trend term and residual term;

[0066] S3: performing secondary exponential smoothing on the residual term, inputting the smoothed residual term into a type of product-sum model to calculate the spatiotemporal variogram, and fitting the spatiotemporal Kriging model according to the spatiotemporal variogram;

[0067] S4: Use the spatiotemporal Kriging model to estimate the data to be filled and obtain an interpolation prediction result.

[0068] Next, combine Figure 1 , a method for interpolating and predicting missing data of a road environment disclosed in this embodiment is described in detail. 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 of an actual road environment.

[0069] 1. Data preparation and preprocessing

[0070] 1. Collect road environment data and process the data in a format that ensures the data is in a unified format, including time, spatial coordinates (latitude and longitude) and measurement values.

[0071] 2. Visualization processing is performed based on the road environment data in a unified format. The distribution, trend and periodicity of the data can be obtained by drawing scatter plots, time series graphs, etc.

[0072] It should be noted that operations such as visualizing data and drawing scatter plots and time series graphs are all conventional technical means well known to those skilled in the art, and their specific implementation methods will not be described in detail here.

[0073] 3. Preprocess the data based on its distribution, trend and periodicity.

[0074] If outliers appear (for example, data points that are significantly deviated from the area where most of the data is located in a scatter plot or other visualization chart), remove the outliers.

[0075] If an overall trend appears, detrend it. For example, when studying the impact of changes in vegetation cover on humidity in a road area, if the humidity data itself has an increasing trend year by year due to climate change, directly building a model may attribute this trend to the impact of changes in vegetation cover, while in fact this part of the impact is caused by other macro factors. Detrending (differential method, decomposition method, etc.) can separate this trend factor, allowing the model to focus more on studying the real relationship between variables.

[0076] If periodicity occurs, a suitable spatiotemporal model can be constructed to extract the periodic characteristics. For example, for road traffic flow data, if there is traffic flow data with a daily or weekly cycle, a corresponding spatiotemporal model with a daily or weekly cycle can be constructed to more accurately predict traffic flow. By capturing the potential law of periodicity, a reference basis can be provided for subsequent data filling.

[0077] 4. Since the training of the spatiotemporal regression model required for this embodiment requires a complete data set, it is necessary to preliminarily identify missing values. Through simple interpolation or neighboring value filling, the data set can be made complete in form, so that preliminary training and parameter estimation of methods such as spatiotemporal regression models can be carried out to ensure the smooth modeling of subsequent spatiotemporal Kriging models.

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

[0079] 5. The additive model in time series decomposition is used to extract the seasonal factors in the preprocessed road environment sample data to remove the seasonal factors. The formula of the additive model is:

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

[0081] Among them, Y t is the observed value of the time series; T tis the trend component; S t is the seasonal component; R t is a random component.

[0082] like Figure 2 This is a schematic diagram of the comparison of de-seasonal data for a site (data collection location). After removing the seasonal factors, the road environment sample data is:

[0083] P t =T t +R t

[0084] Among them, P t is the seasonal road environment sample data, T t is the trend component; R t is a random component.

[0085] (II) Establish a regression model and calculate residuals

[0086] First, the regression model is used to fit the trend term of the preprocessed data, that is, the trend of the data changing with space and time is estimated through linear regression or other regression models.

[0087] Specifically, given the observation value Z(s,t), decompose it into the trend term m(s,t) and the residual term ε(s,t):

[0088] Z(s,t)=m(s,t)+ε(s,t)

[0089] Among them, s represents the spatial position and t represents the time.

[0090] The trend term m(s, t) can be estimated using a regression model. In this embodiment, a multiple linear regression model is preferably used:

[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 time (different time), spatial location (different location), environmental factors (such as temperature, humidity, etc.) and other related variables; β i is the regression coefficient.

[0093] In this embodiment, temperature observation data is selected as an example. For the temperature observation data along a certain highway, s represents different locations on the highway (such as kilometers from the starting point), t represents different times of the day (such as every hour), and f represents the time of day (such as every hour). i (s, t) represents the temperature value at a certain location on the road 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] Among them, s represents the spatial position and t represents the time.

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

[0098] Furthermore, after obtaining the trend term and the residual term, the residual term is analyzed. The residual is evaluated to intuitively understand the degree of deviation between the model prediction value and the actual observation value, and then judge the reliability of the model.

[0099] Specifically, the quality of the regression model is judged by calculating the autocorrelation of the residuals. Figure 3 This is the autocorrelation graph of one of the sites. Most of them are within the confidence interval, and those that are not within the confidence interval do not exceed the range of 0.25, which proves that the regression model has good goodness of fit and stability.

[0100] Subsequently, in order to obtain a smoother residual sequence that can better reflect the internal laws of the residual term and has less noise influence, the residual term is subjected to secondary exponential smoothing, and its basic formula is mainly divided into two parts: the horizontal component and the trend component.

[0101] First, for the horizontal component:

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

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

[0104] Second, for the trend component:

[0105] T t =β(L t -L t-1)+(1-β)T t-1

[0106] Among them, T t is the trend component estimate at the current time t; β is the trend smoothing constant, which is used to control the trend response; L t -L t-1 It represents the change between the current time t and the time t-1 when the horizontal component is estimated, which is used to reflect the change of the horizontal trend.

[0107] After that, the smoothed residual term is expressed as:

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

[0109] Among them, Y t+h is the smoothed residual term, and is the predicted value of the residual term 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 is the residual data before smoothing.

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

[0114] Table 1 Comparison of standard deviations of original data and data after double exponential smoothing

[0115]

[0116] Combination Figure 4 The schematic diagram of the comparison of residual data before and after the second exponential smoothing is shown. It can be clearly seen that the residual noise after the second exponential smoothing is significantly reduced.

[0117] This embodiment uses the quadratic exponential smoothing method to reduce the impact of random noise in the residuals by smoothing historical data, making the potential patterns in the residuals clearer. In addition, the quadratic exponential smoothing method is simple to calculate and is suitable for processing large-scale spatiotemporal data. In particular, when the model needs to be updated quickly, it can efficiently process residuals, that is, the quadratic exponential smoothing method can effectively improve the calculation efficiency and prediction accuracy while maintaining the flexibility of the model.

[0118] 3. Selection of spatiotemporal variation function

[0119] Firstly, the temporal variogram and spatial variogram are constructed based on the residuals, and the temporal and spatial correlations of the residuals are verified by drawing the corresponding variograms.

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

[0121]

[0122] Where γ(h) is the spatial variogram; N(h) is the number of observation pairs with distance h; Z(x i ) is at position x i Observation value; h is the spatial distance.

[0123] Based on the spatial variation function, the following Figure 5 The spatial variogram shown is Figure 6 The ideal spatial variogram fitting image is compared with the Figure 5 and Figure 6 The corresponding curves fit well, indicating that the residuals have spatial correlation.

[0124] The time variogram is constructed based on the residuals. The formula of the time variogram is as follows:

[0125]

[0126] Where γ(τ) is the time variogram; N(τ) is the number of observation pairs with a time interval of τ; Z(t i ) is the time point t i ; τ is the time interval.

[0127] Based on the time variation function, the following Figure 7 The time variation function diagram shown is Figure 6 The ideal time variogram fitting image is compared with the Figure 7 and Figure 8 The corresponding curves fit well, indicating that the residuals have time correlation.

[0128] It should be understood that when the distribution of data points in the variogram drawn based on the residuals can be close to (within a reasonable error range) the ideal variogram image ( Figure 6 or Figure 8 ) can be called "matching". For example, in the spatial variogram, if most of the data points fall around the ideal spatial variogram curve, and the distance between these points and the curve is small (which can be judged by setting a reasonable error threshold, such as the root mean square error is less than a certain value), it means that the two are consistent; similarly, for the time variogram, if the data points and the ideal time variogram curve show a similar degree of proximity at the corresponding time interval, they can also be considered to be consistent.

[0129] After the residuals are determined to have spatiotemporal correlation through the comparison of the above variograms, the spatiotemporal variogram is constructed based on these spatiotemporal correlated residuals. By quantifying this correlation and expressing it in the form of a function, we can further explore the evolution of the data in the spatiotemporal domain so that this information can be used more effectively in subsequent data analysis, prediction or other related research.

[0130] The space-time variogram is usually used to describe the degree of separation of two points in space and time and the variability between their observed values. Its basic formula is as follows:

[0131]

[0132] where γ(h,τ) is the spatiotemporal variogram, N(h,τ) is the number of observation pairs with a time interval of τ and a spatial interval of h, and Z(x i ,t i ) at time point t i and the spatial point x i The observed value on .

[0133] There are two main categories of research on spatiotemporal variogram models: separable models and inseparable models.

[0134] The separable model is relatively simple, and the commonly used ones are spherical models, exponential models or Gaussian models. They are mainly obtained by combining the time variation function and the space variation function in the form of addition or multiplication, and cannot express the relevant information of time and space well.

[0135] The construction process of the inseparable model is relatively complicated, but it can more effectively express the correlation between variables in time and space. Among them, a type of product-sum model is a commonly used inseparable model, which is expressed 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] Among them, γ st (h s ,h t ), γ s (h s ) and γt (h t ) is the spatiotemporal variogram, spatial variogram and temporal variogram; C t (0), C s (0) is the base value corresponding to the temporal variogram and the spatial variogram. The spatiotemporal variogram provides the correlation structure information of the data in time and space. When constructing the spatiotemporal kriging model, this correlation structure will be used to determine the kriging weights.

[0138] A three-dimensional variogram is drawn for the spatiotemporal variogram constructed based on a type of product-sum model. Fig. 9 If the shape and trend of the three-dimensional variogram match the expected pattern of the ideal space-time variogram, it means that the constructed space-time variogram can reasonably reflect the correlation of the data in time and space.

[0139] Calculate evaluation indicators (such as MAE, RMSE, etc.) and check the goodness of the fitting results using R 2 , AIC or BIC and other indicators to evaluate the adaptability of the model, and verify the rationality and accuracy of the spatiotemporal variation function constructed based on a type of product-sum model. It should be understood that the relevant verification method can be implemented by those skilled in the art.

[0140] In this embodiment, a type of 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 changes in time and spatial correlation of environmental factors such as temperature. Once the model training is completed, the interpolation method based on the spatiotemporal variogram can be quickly applied to missing data points, because the model has quantified the spatiotemporal correlation and can directly infer the value of the missing data based on the information of the known data points.

[0141] Since a type of product-sum model can effectively handle spatiotemporal correlation, it can more accurately describe the changing law of road environment data than a simple separable model. By calculating evaluation indicators such as MAE and RMSE, as shown in Table 2, compared with other models, the RMSD of the product-sum model is 0.0101. The low RMSD value means that the average deviation between the predicted value and the true value is extremely small, almost negligible, and can accurately fit the actual observed data; MAE is 8.04, indicating that the model shows extremely high accuracy when fitting road environment data. Therefore, the spatiotemporal variation function based on the product-sum model can provide more accurate results when filling in data, reduce filling errors, and thus better reflect 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 can capture the temporal and spatial correlation of data well. However, in order to accurately interpolate and predict missing data in the road environment, it is necessary to further use these spatiotemporal variograms to construct a spatiotemporal Kriging model.

[0145] 4. Real-time interpolation of space-time Kriging model

[0146] Space-time kriging models rely on accurate space-time variograms for prediction and interpolation.

[0147] 1. Data identification and data processing

[0148] First, the missing values ​​and outliers of the real-time data to be filled are identified. For the temperature data in the road environment, it is assumed that multiple temperature monitoring points are set up along a highway to collect temperature data at different times and locations. For missing values, the interpolation method can be used directly for temporary interpolation; for outliers that exceed the calibration range, they need to be deleted first, and then interpolated using the interpolation method for temporary interpolation, so as to obtain a complete data set without missing values ​​and outliers.

[0149] Then, based on the above data set, the trend term m(s, t) of the missing area is calculated using the multivariate linear regression model.

[0150] 2. Spatiotemporal Kriging Estimation

[0151] After calculating the trend term m(s, t) of the missing area, the residual of the missing area is estimated by spatiotemporal kriging based on the constructed spatiotemporal regression kriging model. That is, given the spatial point and time point (s0, t0) of the missing area, the residual value is estimated by kriging method The announcement is as follows:

[0152]

[0153] Among them, λ i is the spatiotemporal kriging weight, which is obtained by the kriging system equation. The kriging system equation is:

[0154]

[0155] Among them, γ((s i ,t i ),(s j ,t j )) is a spatiotemporal variogram constructed based on a type of product-sum model and determined at a spatiotemporal point (s i ,t i ) and (s j ,t j), for temperature data, it reflects the correlation strength between the data at these two time and space points, and is then 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 of the spatiotemporal kriging estimate Combination, seasonal ingredients t Add the noise d removed by quadratic exponential smoothing to obtain the Kriging interpolation of the road environment data at the final missing location The predicted value has the characteristics of high precision and can effectively repair the missing position. The specific formula is as follows:

[0158]

[0159] In this specific embodiment, the application of spatiotemporal regression kriging is mainly reflected in repairing the missing road environment data and improving the prediction accuracy. The previous time series decomposition removes seasonal factors, and then multiple linear regression is used to capture the overall trend and separate the residual term; the residual term is subjected to the quadratic exponential smoothing method to reduce noise, further extract the time trend, and enhance the filling accuracy; then, the spatiotemporal variation function is constructed based on a type of product-sum model to fully consider the interaction between time and space and better capture the data characteristics. Through regression analysis, the relationship between time and space and road environment data can be established, and then the value of missing and erroneous data can be predicted through the existing time and space data; in addition, when processing the collected data, the data is first preprocessed, and then the regression model is applied to capture the trend, calculate the residual, and then the spatiotemporal kriging is used to interpolate these residuals, so as to obtain more accurate road environment data. This method not only reduces the uncertainty caused by missing data, but also improves the overall evaluation of the road environment.

[0160] Embodiment 2

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

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

[0163] The regression fitting module is used to take the deseasonalized road environment sample data as observation values, input them into the multivariate linear regression model for fitting, and obtain the trend term and residual term;

[0164] A function and model building module, for performing secondary exponential smoothing on the residual term, inputting the smoothed residual term into a type of product-sum model to calculate the spatiotemporal variogram, and fitting the spatiotemporal Kriging model according to the spatiotemporal variogram;

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

[0166] Embodiment 3

[0167] This embodiment provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps in the method for interpolating and predicting missing data in a road environment as described in the first embodiment above are implemented.

[0168] Embodiment 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, the steps in a method for interpolating and predicting missing data in a road environment as described in the first embodiment above are implemented.

[0170] The steps or modules involved in the above embodiments 2 to 4 correspond to those in embodiment 1. For the specific implementation, please refer to the relevant description 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 to include any medium that can store, encode or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0171] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for interpolating and predicting missing data of a road environment, characterized in that: include: Obtain road environment sample data, perform preprocessing and remove seasonal factors; The deseasonalized road environment sample data are used as observation values ​​and input into the multivariate linear regression model for fitting to obtain the trend term and residual term. Performing quadratic exponential smoothing on the residual term, inputting the smoothed residual term into a type of product-sum model to calculate the spatiotemporal variogram, and fitting the spatiotemporal Kriging model according to the spatiotemporal variogram; The space-time Kriging model is used to estimate the data to be filled and obtain the interpolation prediction result.

2. A method for interpolating and predicting missing data of a road environment according to claim 1, characterized in that: The preprocessing includes: processing the road environment sample data in a unified format and deleting abnormal values ​​based on a calibration range.

3. The method for interpolating and predicting missing data of a road environment according to claim 1, characterized in that: The removal of seasonal factors specifically includes: using an additive model in the time series decomposition method to remove seasonal factors in the road environment sample data.

4. A method for interpolating and predicting missing data of a road environment as claimed in claim 1, characterized in that: The deseasonalized road environment sample data is used as observation values ​​and input into a multiple linear regression model for fitting to obtain trend terms 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: m(s,t)=β0+β1f1(s,t)+β2f2(s,t)+…+β p f p (s,t) Among them, f i (s, t) represents the independent variable, β i represents the regression coefficient; The estimated trend term is subtracted from the observed value to obtain the residual term; the residual term ε(s, t) is: ε(s,t)=Z(s,t)-m(s,t) Among them, Z(s,t) represents the observation value, m(s,t) represents the trend term, s represents the spatial position, and t represents the time.

5. The method for interpolating and predicting missing data of a road environment according to claim 1, characterized in that: The performing of secondary exponential smoothing on the residual term specifically includes: Y t+h =L t +hT t L t =αY t +(1-α)(L t-1 +T t-1 ) T t =β(L t -L t-1 )+(1-β)T t-1 Among them, Y t+h is the smoothed residual term, which is the predicted value of the residual term at time t+h; L t is the horizontal component estimate at the current time t, T t Y is the trend component estimate at the current time t; t is the actual observed value of the residual term at the current time t; α is the horizontal smoothing constant, which is used to control the response to the current observed value of the residual term; L t-1 is the horizontal 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 It represents the change between the current time t and the time t-1 when the horizontal component is estimated, which is used to reflect the change of the horizontal trend.

6. A method for interpolating and predicting missing data of a road environment as claimed in claim 1, characterized in that: The step of inputting the smoothed residual term into a product-sum model to calculate the spatiotemporal variogram specifically includes: c st (h,τ)=[k1C t (0)+k2]γ(h)+[k1C s (0)+k3]γ(τ)-k1γ(h)γ(τ) Among them, 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) is the base value corresponding to the temporal variogram and spatial variogram; N(h) is the number of observation pairs with distance h; Z(x i ) is at position x i The observed value; h is the spatial distance; N(τ) is the number of observation pairs with a time interval of τ; Z(t i ) is the time point t i ; τ is the time interval, k1, k2, k3 are model parameters.

7. The method for interpolating and predicting missing data of a road environment according to claim 1, characterized in that: The method of using the spatiotemporal Kriging model to estimate the data to be filled and obtain the interpolation prediction result specifically includes: Among them, ε(s i ,t i ) is the residual term of the data to be filled, is the estimated residual term, λ i is the spatiotemporal Kriging weight, obtained by the Kriging system equation; the Kriging system equation is: Among them, γ((s i ,t i ),(s j ,t j )) is a spatiotemporal variogram constructed based on a type of product-sum model and determined at a spatiotemporal point (s i ,t i ) and (s j ,t j ) between the values ​​of variation; The trend term m(s, t) of the data to be filled and the estimated residual term Seasonal ingredients t Combined with the noise d removed by quadratic exponential smoothing, the restored road environment data is obtained: d=Y t+h -Y t Among them, Y t+h is the residual term after smoothing, Y t is the residual data before smoothing.

8. A road environment missing data interpolation prediction system, characterized in that: include: The data acquisition module is used to obtain road environment sample data, perform preprocessing and remove seasonal factors; The regression fitting module is used to take the deseasonalized road environment sample data as observation values, input them into the multivariate linear regression model for fitting, and obtain the trend term and residual term; A function and model building module, for performing secondary exponential smoothing on the residual term, inputting the smoothed residual term into a type of product-sum model to calculate the spatiotemporal variogram, and fitting the spatiotemporal Kriging model according to the spatiotemporal variogram; The interpolation prediction module is used to estimate the data to be filled using the spatiotemporal Kriging model to obtain an interpolation prediction result.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in a method for interpolating and predicting missing data in a road environment as described in any one of claims 1 to 7 are implemented.

10. 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, the steps in the method for interpolating and predicting missing data in a road environment as described in any one of claims 1-7 are implemented.

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