CN111259537B - Road surface performance prediction method based on VAR (variable-value response) multivariate time sequence - Google Patents
Road surface performance prediction method based on VAR (variable-value response) multivariate time sequence Download PDFInfo
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Abstract
The invention discloses a road surface performance prediction method based on a VAR multivariate time sequence, which comprises the following steps: step 1), dividing road sections; step 2), selecting a plurality of pavement performance indexes; step 3), analyzing the influence of correlation of the road surface index based on the VAR; and 4) establishing a road surface performance index prediction model. The step 3) comprises the following steps: step 3.1), a VAR model is established for the road surface performance indexes with long-term correlation, and the influence among the road surface performance indexes is analyzed through variance decomposition; and 3.2) selecting the pavement performance indexes which have influence on the pavement performance indexes exceeding the preset percentage value as predicted pavement performance indexes, and screening out other pavement performance indexes. The pavement performance prediction method based on the VAR multivariate time sequence screens the factors with the predicted performance by applying the numerical analysis aiming at the correlation among the factors in the VAR multivariate time sequence, thereby greatly improving the accuracy of pavement performance prediction and the reliability when being applied to pavement preventive maintenance decision.
Description
Technical Field
The invention relates to the technical field of road monitoring, in particular to a road surface performance prediction method based on a VAR (variable-value automatic response) multivariate time sequence.
Background
The prediction of the road performance has crucial significance for the implementation of preventive maintenance. The traditional single variable time sequence pavement performance prediction method can only predict a future value according to the historical change of a certain pavement performance index, and neglects other influence factors. In the future, a certain road surface performance index is usually related to the current value of the performance index and other road surface performance indexes. Therefore, if various road surface performance index values are taken into consideration at present, the mathematical model is used for prediction, and the model precision can be improved.
Therefore, the invention provides a road surface performance prediction method adopting a multivariate time sequence. The VAR model is most commonly used in the multivariate time sequence, and the current-stage value is predicted by carrying out regression on the same-order lag variables of all variables, so that the dynamic relation among the endogenous variables can be estimated, and the influence of the exogenous variables on the endogenous variables can be reflected. In order to further ensure the prediction accuracy of the model, the VAR model is firstly adopted to analyze the influence effect among variables, and a brand-new multivariate time sequence prediction method is constructed based on the analysis result of the influence effect, so that the disturbance effect of various factors on the road performance is comprehensively analyzed, and the performance of the road performance prediction model is improved.
Disclosure of Invention
The invention aims to provide a road surface performance prediction method based on a VAR multi-element time sequence, and the accuracy and the reliability of road surface performance prediction are improved.
In order to achieve the purpose, the road surface performance prediction method based on the VAR multivariate time sequence comprises the following steps: step 1), dividing road sections;
step 2), selecting a plurality of pavement performance indexes;
step 3), analyzing the influence of correlation of the road surface index based on the VAR;
step 4), establishing a road surface performance index prediction model;
the step 3) further comprises the following steps:
step 3.1), building a VAR model for the pavement performance indexes with long-term correlation, and analyzing the influence among the pavement performance indexes through variance decomposition;
and 3.2) selecting the pavement performance indexes which have influence on the pavement performance indexes exceeding the preset percentage value as predicted pavement performance indexes, and screening out other pavement performance indexes.
Preferably, in step 3.2), AIC calculation is performed on the road surface performance indexes with long-term correlation by using different p values of autoregressive coefficients, a p value corresponding to the smallest AIC value is selected, a VAR (p) model is constructed, and the influence between the road surface performance indexes is obtained through variance decomposition.
Preferably, in the step 3.2), the preset percentage value is 10%.
As a preferable scheme, in the step 4), different autoregressive coefficient p values are adopted to perform AIC calculation, the autoregressive coefficient p value corresponding to the minimum AIC value is taken to construct a VAR (p) model, and data of the original road surface performance index is substituted into data for calculating the future road surface performance index.
Preferably, the step 1) further comprises the following steps:
step 1.1), extracting original data of a plurality of pavement performance indexes of the current pavement from a database;
and 1.2) dividing the original pavement performance index into equidistant road sections according to the same factors in a datamation mode.
Preferably, in step 1.1), the original data of the road surface performance indexes extracted from the database are arranged according to the year, when multiple groups of data appear in the same year, the multiple groups of data are averaged, and if data are missing, the data are supplemented by an interpolation method.
Preferably, in the step 1.2), the factors comprise the same structure, the same curing measures and time, and the equal distance is 100 meters.
Preferably, the step 2) further comprises the following steps:
step 2.1), carrying out stability inspection on the original data of a plurality of road surface performance indexes in the road section, if not, carrying out differential calculation until the stability inspection is passed;
and 2.2) performing collaborative analysis on the data of the plurality of road surface performance indexes which pass the stability test, and selecting the road surface performance indexes with long-term correlation as predicted road surface performance indexes.
Preferably, in the step 2.1), performing stability ADF inspection on the road surface performance index data in the road section, if not, performing differential calculation until a stability inspection result is less than 0.05; in the step 2.2), when the road surface performance index passing stability test is subjected to the coordination test result of less than 0.05, the road surface performance index data is considered to have long-term correlation and is determined as the road surface performance index for prediction.
Preferably, the predicted road surface performance indexes are PCI, IRI and RD;
the variation Δ IRI of the IRI prediction time is calculated according to the following formula:
ΔIRI(t)＝-0.0426IRI(t-1)+0.1202ΔRD(t-1)；
the change value Δ RD at the RD predicted time is calculated according to the following equation:
ΔRD(t)＝4.9184IRI(t-1)+0.1939ΔRD(t-1)；
the change Δ RD at the PCI predicted time is calculated according to the following equation:
ΔPCI(t)＝-2.3529ΔIRI(t-1)-0.5323ΔRD(t-1)+0.4575PCI(t-1)；
where t denotes the predicted time and t-1 denotes the previous time at an interval of t.
The beneficial effects of the invention are: according to the pavement performance prediction method based on the VAR multivariate time sequence, the factors with the predicted performance are screened by using numerical analysis aiming at the correlation among the factors in the VAR multivariate time sequence, so that the accuracy of pavement performance prediction and the reliability when the method is applied to pavement preventive maintenance decision are greatly improved.
Drawings
Fig. 1 is a flowchart of a road surface performance prediction method based on VAR multivariate time series according to a preferred embodiment of the present invention.
Fig. 2 is a comparison graph before and after an IRI predicted value is performed by using the VAR multivariate time series-based road surface performance prediction method according to the preferred embodiment of the present invention.
Fig. 3 is a comparison graph before and after the RD prediction value is performed by using the road surface performance prediction method based on VAR multivariate time series according to the preferred embodiment of the present invention.
FIG. 4 is a diagram of PCI unit and multivariate time series prediction value comparison.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
In order to solve the problems, the invention provides a road surface performance prediction method based on a VAR multivariate time sequence. VAR (Vector Auto Regression) is commonly used to predict interconnected time series systems and to analyze the dynamic effects of random perturbations on variable systems. The VAR circumvents the need to structure the model by constructing the model with each endogenous variable in the system as a function of the hysteresis values of all endogenous variables in the system.
The road surface performance prediction method based on the VAR multivariate time sequence firstly adopts the VAR model to analyze the influence effect among variables, and a brand new multivariate time sequence prediction method is constructed on the basis, so that the time sequence prediction precision can be improved.
Please refer to fig. 1, which is a schematic flow chart of a road surface performance prediction method based on VAR multivariate time series according to a preferred embodiment of the present invention, including the following steps: step 1), road section division; step 2), selecting a plurality of pavement performance indexes; step 3), analyzing the influence of correlation of the road surface indexes based on the VAR; and 4) establishing a road surface performance index prediction model.
Wherein, in the step 1), the method specifically comprises the following steps:
step 1.1), extracting the original data of a plurality of pavement performance indexes of the current pavement from the database.
Extracting original data of a plurality of pavement performance indexes of the current pavement from a database, arranging various performance data according to the year, and averaging the plurality of groups of data when the plurality of groups of data appear in the same year.
Step 1.2), dividing the road sections into sections of 100 meters per section according to the factors of the same structure, the same maintenance measures, time and the like.
The road sections are divided into sections of 100 meters each according to the factors of the same structure, the same maintenance measures, time and the like.
And 1.3) if data are missing, supplementing the data through an interpolation method, such as an average value method.
If data loss occurs in a certain year, the data is supplemented by an interpolation method of averaging the previous value and the next value.
Wherein, in the step 2), the method specifically comprises the following steps:
and 2.1) carrying out stability inspection on the original data of a plurality of road surface performance indexes in the road section, if not, carrying out differential calculation until the stability inspection is passed.
And (3) carrying out stability ADF (automatic document feeder) inspection (unit root inspection) on various performance data in the road section, if the performance data are not stable, carrying out differential calculation until the stability inspection is passed, namely, the inspection result p-value is less than 0.05.
And 2.2) performing collaborative analysis on the multiple road surface performance index data passing through the stability test, and selecting the road surface performance index having a long-term correlation relationship.
And performing co-integration inspection on the various types of performance data passing the stability inspection, and when the inspection result p-value is less than 0.05, determining that the performance data have long-term correlation and determining the performance data as the road surface performance index for modeling.
Wherein, in the step 3), the method specifically comprises the following steps:
and 3.1) establishing a VAR model for the pavement performance indexes with long-term correlation, and analyzing the influence effect among all factors through variance decomposition.
And for the road surface performance indexes with long-term correlation, different autoregressive coefficient p values are adopted to carry out AIC calculation, the p value corresponding to the minimum AIC value is taken to construct a VAR (p) model, and the influence effect of each road surface performance index on each other is obtained through variance decomposition.
And 3.2) selecting other road surface performance indexes which have influence on the road surface performance index to be predicted over a certain percentage value, considering that the road surface performance index over the percentage value is effective on the predicted road surface performance index, and screening out the other road surface performance indexes as bad disturbance.
And selecting other road surface performance indexes which have more than 10% influence on the road surface performance index to be predicted, considering that the road surface performance index which exceeds the value is beneficial to improving the prediction result on the predicted road surface performance index, and screening out the other road surface performance indexes as bad disturbance.
In the step 4), a VAR model based on the screened road surface performance index data is constructed, and future road surface performance data is predicted.
And (2) adopting an AIC information criterion (Akaike information criterion) and adopting different autoregressive coefficient p values to calculate AIC, and taking the autoregressive coefficient p value corresponding to the minimum AIC value to construct a VAR (P) model, and substituting original data to realize the prediction of future pavement performance index data.
The following is an application of the road surface performance prediction method based on the VAR multivariate time sequence in a specific example.
And step 1), assuming basic data, carrying out time sequence arrangement and road section division.
And 2) selecting IRI (international flatness index), RD (track depth) and PCI (road surface condition index) data in the road section performance.
ADF inspection is carried out on the three types of data, and the data p-value >0.05 in the original time sequence is found, and the data is not stable, so that the data is subjected to first-order difference, inspected again and passed. And carrying out pairwise integration test on IRI, RD and PCI data, wherein p-value is less than 0.05, and long-term correlation exists between the IRI, RD and PCI data.
The VAR (1) model was constructed by performing AIC calculation on a VAR model with an autoregressive coefficient p =0,1 and finding that the AIC is the minimum value when the autoregressive coefficient p = 1.
And 3) calculating to obtain the relevant parameters of the VAR model, and obtaining the influence effect of each road surface performance index on each other by adopting variance decomposition.
ΔIRI(t)＝-0.2085ΔIRI(t-1)+0.1055ΔRD(t-1)-0.0243PCI(t-1)；
ΔRD(t)＝2.1674ΔIRI(t-1)-0.0784ΔRD(t-1)-0.4440PCI(t-1)；
ΔPCI(t)＝-2.3529ΔIRI(t-1)-0.5323ΔRD(t-1)+0.4575PCI(t-1)。
Wherein t represents the time corresponding to the solved road surface performance index, and t-1 represents the last time spaced from the time t. Typically, t is the year and t-1 is the last year.
For this model, the effect of the various road surface performance indicators on each other can be obtained by variance decomposition, as shown in table 1.
TABLE 1 Effect of various pavement Performance indicators on each other
Therefore, it is considered that the IRI and RD can be predicted from each other, and the predicted result of PCI is still determined by IRI, RD and PCI.
The VAR model (1) was constructed by performing AIC calculation on the IRI and RD VAR models with an autoregressive coefficient p =0,1 and finding that the minimum AIC is obtained when the autoregressive coefficient p = 1.
And 4), calculating to obtain VAR model related parameters to obtain a VAR model related formula.
ΔIRI(t)＝-0.0426IRI(t-1)+0.1202ΔRD(t-1)；
ΔRD(t)＝4.9184IRI(t-1)+0.1939ΔRD(t-1)。
For this model, the change values Δ IRI, Δ RD of the future year can be predicted, and compared with the predicted result in the previous step, see fig. 2 and fig. 3.
Because PCI and PCI, IRI, RD all have comparatively close relation, PCI prediction formula after screening still is:
ΔPCI(t)＝-2.3529ΔIRI(t-1)-0.5323ΔRD(t-1)+0.4575PCI(t-1)。
therefore, a unit time sequence prediction is used to compare with a multi-element time sequence prediction result of the PCI, and an ARIMA (p, l, q) model (differential Integrated Moving Average Autoregressive model, also called Integrated Moving Average Autoregressive model) of the unit time sequence is established. Where p denotes an autoregressive coefficient, l denotes a difference order, and q denotes a moving average coefficient. Firstly, obtaining a stable PCI time sequence through difference, secondly, selecting different (p, q) values to carry out AIC calculation, and constructing an ARIMA model by taking an autoregressive coefficient p and a moving average coefficient q corresponding to the minimum AIC value. Through the difference sequence stationary discrimination and the AIC criterion, the formula for obtaining the unit time sequence ARIMA (3, 1) is as follows:
ΔPCI(t)-0.3858ΔPCI(t-1)-0.6502ΔPCI(t-2)-0.4981ΔPCI(t-3)-1ε(t-1)-1.7214。
for this model, the PCI values in the time series of units for the future year can be predicted, see fig. 4.
Compared with the traditional unit or multivariate time sequence, the pavement performance prediction method based on the VAR multivariate time sequence screens the factors with prediction performance by applying numerical analysis on the correlation among the factors in the VAR multivariate time sequence, thereby greatly improving the accuracy of pavement performance prediction and the reliability when being applied to pavement preventive maintenance decision.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that various changes and modifications can be made by those skilled in the art without departing from the spirit of the invention, and these changes and modifications are all within the scope of the invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (8)
1. A road surface performance prediction method based on VAR multi-element time sequence comprises the following steps:
step 1), dividing road sections;
step 2), selecting a plurality of pavement performance indexes;
step 3), analyzing the influence of correlation of the road surface index based on the VAR;
step 4), establishing a road surface performance index prediction model;
the step 3) further comprises the following steps:
step 3.1), a VAR model is established for the road surface performance indexes with long-term correlation, and the influence among the road surface performance indexes is analyzed through variance decomposition;
step 3.2), selecting the pavement performance indexes which have influence on the pavement performance indexes exceeding the preset percentage value as predicted pavement performance indexes, and screening out other pavement performance indexes;
in the step 4), different autoregressive coefficient p values are adopted to perform AIC calculation, the autoregressive coefficient p value corresponding to the minimum AIC value is taken to construct a VAR (p) model, and the data of the original pavement performance index is brought into the calculation of the future pavement performance index data;
wherein the predicted road surface performance indexes are PCI, IRI and RD;
the variation Δ IRI at the IRI prediction time is calculated according to the following formula:
ΔIRI(t)＝-0.0426IRI(t-1)+0.1202ΔRD(t-1)；
the change value Δ RD at the RD prediction time is calculated according to the following equation:
ΔRD(t)＝4.9184IRI(t-1)+0.1939ΔRD(t-1)；
the change Δ RD at the PCI predicted time is calculated according to the following equation:
ΔPCI(t)＝-2.3529ΔIRI(t-1)-0.5323ΔRD(t-1)+0.4575PCI(t-1)；
where t denotes the predicted time and t-1 denotes the last time at an interval of one from t.
2. The VAR multivariate time series-based road surface performance prediction method as defined in claim 1, wherein: in the step 3.2), different autoregressive coefficient p values are adopted to perform AIC calculation on the road surface performance indexes with long-term correlation, the p value corresponding to the minimum AIC value is taken to construct a VAR (p) model, and the influence among the road surface performance indexes is obtained through variance decomposition.
3. The VAR multivariate time series-based road surface performance prediction method as defined in claim 1, wherein: in the step 3.2), the preset percentage value is 10%.
4. The VAR multivariate time series-based road surface performance prediction method as defined in claim 1, wherein: the step 1) further comprises the following steps:
step 1.1), extracting original data of a plurality of pavement performance indexes of the current pavement from a database;
and 1.2) dividing the original pavement performance index into equidistant road sections according to the same factors in a datamation mode.
5. The VAR multivariate time series-based road surface performance prediction method as set forth in claim 4, wherein: in the step 1.1), the original data of the pavement performance indexes are extracted from the database, the various performance data are arranged according to the year, when multiple groups of data appear in the same year, the multiple groups of data are averaged, and if data are missing, the data are supplemented through an interpolation method.
6. The VAR multivariate time series-based road surface performance prediction method as defined in claim 4, wherein: in step 1.2), the factors include the same structure, the same maintenance measures and time, and the equal distance is 100 meters.
7. The VAR multivariate time series-based road surface performance prediction method as defined in claim 1, wherein: the step 2) further comprises the following steps: step 2.1), carrying out stability inspection on the original data of a plurality of road surface performance indexes in the road section, if not, carrying out differential calculation until the stability inspection is passed;
and 2.2) performing collaborative analysis on the data of the plurality of road surface performance indexes passing the stability test, and selecting the road surface performance indexes with long-term correlation as predicted road surface performance indexes.
8. The VAR multivariate time series-based road surface performance prediction method according to claim 7, characterized in that: in the step 2.1), stability ADF inspection is carried out on the road surface performance index data in the road section, if the road surface performance index data are not stable, differential calculation is carried out until a stability inspection result is less than 0.05; in the step 2.2), when the road surface performance index passing stability test is subjected to the coordination test result of less than 0.05, the road surface performance index data is considered to have long-term correlation and is determined as the road surface performance index for prediction.
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