CN112529386B - Quantitative determination method for usability of asphalt pavement - Google Patents
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Abstract
The invention discloses a quantitative determination method for the service performance of an asphalt pavement, which specifically comprises the following steps: collecting pavement service performance parameters, and recording the pavement service performance parameters as a parameter sample X 1,X2,X3,X4; determining prior probabilities q i of different performance evaluation grades according to the road surface use performance evaluation results corresponding to the known multiple groups of parameter samples, wherein the parameter samples corresponding to the road surface use performance evaluation grades, namely a classification overall G i; determining a discrimination function coefficient of the pavement using performance evaluation level, and constructing a discrimination function; determining the evaluation level of the using performance of other asphalt pavements through a discriminant function according to the evaluation level of the discriminant function return judgment and inspection classification ensemble G i; and calculating the grade probability that the parameter samples of the corresponding asphalt pavement belong to different classification totalities G i, and quantitatively representing the service performance of the corresponding asphalt pavement. The invention considers the difference of each parameter of the asphalt pavement, reduces the influence of subjective factors, improves the efficiency, scientificity and reliability of determining the service performance of the asphalt pavement, and has excellent universality.
Description
Technical Field
The invention belongs to the technical field of road engineering, and relates to a quantitative determination method for the service performance of an asphalt pavement.
Background
The road surface service performance evaluation is an important link in maintenance management, and is a complex system with a plurality of uncertainty factors, wherein the uncertainty contains a large amount of information such as randomness, ambiguity, ash property, uncertainty and the like, and the mutual relationship is complex, so that the comprehensive quantification can not be realized. Scientific and accurate evaluation of pavement service performance is the basis and key for scientifically and effectively implementing pavement maintenance. The existing mode is developed by using mathematical methods such as analytic hierarchy process, fuzzy mathematical method, neural network method, interval number approximation method, principal component analysis method, mutation theory and the like, the rationality of evaluation is improved, but in the multiple problems of evaluating the reliability of the pavement service performance, the probability of classifying each grade or evaluating the result cannot be known, and the quantitative characterization of the pavement service performance is difficult to realize. The prior art has the following problems:
(1) Factors influencing the service performance of the pavement comprise various parameters such as vehicle load, temperature, humidity, construction quality and the like, and have certain randomness and uncertainty, so that the service performance of the pavement is different. According to the current road technical condition evaluation standard, the evaluation of the using performance of the asphalt pavement is a deterministic evaluation method of given weight, the influence of the difference of each index on the weight is not considered, the grading of the evaluation indexes is not considered, the formed pavement evaluation result is hard division, and the evaluation scientificity is required to be improved.
(2) The basic idea of reliability analysis of pavement performance by using the reliability is that the reliability is higher as the evaluation value is smaller than a threshold value and the absolute distance between the evaluation value and the threshold value is larger, the reliability of the system is generally represented by the result, but in the process of determining the pavement performance, the probability calculation of each performance evaluation result cannot be represented by the reliability.
Disclosure of Invention
In order to solve the problems, the invention provides the quantitative determination method for the service performance of the asphalt pavement, which fully considers the difference of various parameters of the asphalt pavement, reduces the influence of subjective factors, improves the efficiency, scientificity and reliability of determining the service performance of the asphalt pavement, can quantitatively characterize the service performance of the pavement, has excellent universality and solves the problems in the prior art.
The technical scheme adopted by the invention is that the quantitative determination method for the service performance of the asphalt pavement is carried out according to the following steps:
S1: collecting pavement service performance parameters: the road surface damage condition index PCI, the road surface running quality index RQI, the road rut depth index RDI, and the road surface anti-slip performance index SRI are respectively expressed as a parameter sample X 1,X2,X3,X4, and the total parameter sample is x= (X 1,X2,X3,X4);
S2: determining prior probabilities q i of different performance evaluation grades according to the road surface use performance evaluation results corresponding to the known multiple groups of parameter samples, wherein the parameter samples corresponding to the road surface use performance evaluation grades, namely a classification overall G i;
s3: determining a discrimination function coefficient of the pavement using performance evaluation level, and constructing a discrimination function;
Wi(x)＝xTai+bi
When (when) When x is G i; where a i represents a coefficient vector obtained from the parameter samples of G i, a i＝Σ-1μi;bi represents a constant term obtained from the parameter samples of G i,/>X T represents a transposed matrix of a parameter sample X, where the parameter sample X is a certain set of data of X in step S1, μ i represents a mean vector of G i, and G represents a class of evaluation level;
S4: determining the evaluation level of the use performance of other asphalt pavements by the constructed discriminant function and the evaluation level of the classified population G i by the constructed discriminant function;
S5: according to the basic principle of Bayes discrimination, calculating the grade probability that the parameter sample of the corresponding asphalt pavement in the step S4 belongs to the different classification population G i according to the following formula, and quantitatively representing the service performance of the corresponding asphalt pavement;
wherein: d (x, G i) represents the mahalanobis distance of the parameter sample x to the class ensemble G i;
Σ represents the covariance matrix of each classification ensemble G 1,G2,…Gi,…Gg.
Further, in the step S2, the formula isThe prior probability q i of the classification ensemble G i is calculated, where n i represents the number of parameter samples corresponding to each evaluation level, i=1, 2.
Further, in the step S3, the mean vector μ i of the classification ensemble G i is expressed according to the formulaCalculating; where x k (i) represents the kth sample value of the ith evaluation level,/>I=1, 2, … g, n i is the number of samples of the i-th evaluation level, which is the sample mean.
Further, the step S5 further includes, assuming that the covariance matrices of the classification populations G 1,G2,…Gi,…Gg are equal, i.e. Σ 1＝Σ2＝Σi...＝Σg =Σ, to estimate the classification population G i, calculating according to the following formulaAn estimate of Σ;
wherein S 1,...,Sk,...,Sg is the standard deviation of the sample, X k (i) represents the kth sample value of the ith evaluation level.
Further, the method further comprises the following steps: randomly sampling and arranging a plurality of times in a plurality of known parameter samples, taking one part of arranged samples as learning training samples and the other part of arranged samples as test samples; determining prior probabilities q i of different performance evaluation grades according to road surface use performance evaluation results corresponding to the learning samples, and classifying the overall G i, namely the learning samples corresponding to the road surface use performance evaluation grades; determining the road surface use performance evaluation grade of the test sample through the constructed discriminant function, determining the use performance evaluation grade of other asphalt road surfaces through the constructed discriminant function, determining the grade probability of the asphalt road surface parameter sample, and quantitatively representing the use performance of the corresponding asphalt road surface.
The invention synthesizes the generalized square distance discrimination and the Bayes discrimination criteria to construct the discrimination function and calculate the grade probability, the generalized square distance discrimination considers the grade probability and the difference of the covariance matrix in each group, and the calculation is relatively simple. The Bayesian discrimination considers the difference of appearance (prior probability) of different populations, and the difference of losses caused by each error discrimination and honors the distribution state of each population. When the service performance evaluation grade of a certain road section of a certain asphalt pavement is known, the service performance evaluation grade of other asphalt pavements can be obtained more accurately, and the method can be widely applied to different asphalt pavements; meanwhile, the specific probability that each parameter sample belongs to the corresponding evaluation grade can be calculated through the grade probability, the accuracy and the reliability of the evaluation of the service performance of the asphalt pavement are improved, and the accurate evaluation and quantitative characterization of the reliability grade of the service performance of the asphalt pavement are realized.
The beneficial effects of the invention are as follows:
1. According to the invention, the differentiation of each parameter of the asphalt pavement is fully considered through the discriminant function, so that the influence of subjective factors is reduced, and the scientificity and reliability of the determination of the service performance of the asphalt pavement are improved; the method solves the problem that the reliability of the determination result of the service performance of the asphalt pavement is low due to the fact that the calculation weight of the service performance evaluation of the existing pavement is regarded as a constant and the difference of various parameters of the asphalt pavement is ignored.
2. According to the invention, the specific probability belonging to the corresponding level can be calculated through the calculation model of the level probability, so that quantitative characterization of the pavement using performance is realized; the method provides reliable data for pavement service performance prediction and pavement maintenance decision of the asphalt pavement, and has important application value.
3. The invention can predict the service performance evaluation grades of more asphalt pavements through the calculation model of the discriminant function and the grade probability, has excellent universality, improves the efficiency of determining the service performance of the asphalt pavements, and reduces the labor cost and the time cost.
Detailed Description
The technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention relates to a quantitative determination method for the service performance of an asphalt pavement, which is illustrated by taking a certain road section as an example, and specifically comprises the following steps:
S1: collecting road surface use Performance (PQI) parameters including a road surface damage condition index PCI, a road surface running quality index RQI, a road surface track depth index RDI and a road surface anti-skid performance index SRI, wherein the road surface damage condition index PCI, the road surface running quality index RQI, the road surface track depth index RDI and the road surface anti-skid performance index SRI are shown in table 1;
Table 1 pavement performance test data
S2: calculating prior probabilities of different evaluation grades;
S21: road surface use Performance (PQI) is expressed as X, and subitem indexes PCI, RQI, RDI, SRI of road surface use performance indexes are respectively expressed as parameter samples X 1,X2,X3,X4, and total parameter samples x= (X 1,X2,X3,X4) are taken as discrimination factors;
S22: the road surface use performance evaluation grade was classified into g, and g in Table 1 was equal to 3, and 3 grades corresponding to the road surface use performance evaluation, namely, excellent not less than 90, 80 not less than good < 90, medium < 80, were recorded as evaluation grades 1,2,3. Then determining the evaluation grade of each group of samples according to the collected data by 50 experts; the evaluation grades of table 1 can also be obtained in other ways.
S23: the above 40 sets of parameter samples x= (X 1,X2,X3,X4) are randomly sampled and arranged N times, and the more the number of random sequences, the smaller the influence on the prediction or evaluation result, n=100 in this embodiment; taking the first 30 groups of samples after arrangement as learning training samples and the last 10 groups as test samples, wherein each sample in the population of the investigation object has the same possibility of being pumped, so that the samples have the same structure as the population, or have the greatest possibility that certain characteristics of the population are represented in the samples; in the embodiment, the reliability calculation is performed by adopting random sampling arrangement data, so that calculation errors caused by artificial sequencing are reduced.
S24: the number of samples of different classification populations G 1,G2,G3 in the first 30 groups of parameter samples is n 1＝1,n2＝27,n3 =2, and classification population G 1,G2,G3 is the parameter sample corresponding to road surface use performance evaluation grades 1,2 and 3; the road surfaces use parameter samples corresponding to the performance evaluation grades, namely, classified population G i;
S25: calculating the prior probability q 1 =0.033 of the classification overall G 1 through the formula (1), wherein the prior probability q 2 =0.9 of the classification overall G 2, and the prior probability q 3 =0.067 of the classification overall G 3;
g represents the category of the evaluation rating, n 1+n2...+ng is equal to 30, g=3 in the example.
S3: determining the discrimination function coefficients of different pavement using performance evaluation grades, and constructing a discrimination function;
s31: the mean vectors mu i of different evaluation grades are calculated respectively, as shown in formula (2),
Where x k (i) represents the kth sample value of the ith evaluation level,I=1, 2, … g, n i is the number of samples of the i-th evaluation grade population;
The average vector μ1＝(100,94.04,80.59,82.34)T,μ2＝(93.6144,89.903,77.0644,86.4163)T,μ3＝(93.03,91.23,46.45,82.465)T;μ1 representing the road surface use performance evaluation level 1, μ 2 representing the average vector of the road surface use performance evaluation level 2, and μ 3 representing the average vector of the road surface use performance evaluation level 3 is obtained according to the formula (2).
S32: let the covariance matrices of the respective classification populations G 1,G2,…Gi,…Gg be equal, i.e., Σ 1＝Σ2＝Σi...＝Σg =Σ. Using learning training sample as estimation, calculating according to formula (3)An estimate of Σ;
Where S i(S1,...,Sk,...,Sg) is the sample standard deviation, X k (i) represents the kth sample value of the ith evaluation level ensemble;
S33: constructing a discriminant function in formula (4) according to Bayes discriminant principle,
Wi(x)＝xTai+bi (4)
When (when)When x is G i. Where a i represents the coefficient vector derived from the sample of class population G i, a i＝Σ-1μi;bi represents the constant term derived from the sample of class population G i,/>X T represents a transposed matrix of a parameter sample X, where the parameter sample X is a set of data of X in S21, μ i represents a mean vector of different evaluation levels, and g represents a class of the evaluation level;
S34: solving by using a formula (4) to obtain discriminant function coefficients a i and b i of the three classified totalities, and constructing a discriminant function:
W1(x)＝16.085x1+15.905x2-6.818x3+25.742x4-2340.578
W2(x)＝15.565x1+15.275x2-6.986x3+26.778x4-2303.113
W3(x)＝16.113x1+16.171x2-8.149x3+27.670x4-2441.44 1
X 1、x2、x3、x4 corresponds to PCI, RQI, RDI, SRI, X in S21, respectively 1,X2,X3,X4
W 1(x)、W2(x)、W3 (x) represents the discriminant functions of the three evaluation levels, respectively.
S35: comparing max { W 1(x),W2(x),W3 (x) }, then x ε G i.
S4: the probabilities of the different evaluation grades to which the learning training samples belong (i.e., the probabilities of the grades in table 2) are calculated according to equation (5):
Wherein: d (x, G i) represents the mahalanobis distance of the parameter sample x to the class ensemble G i, i.e. the likelihood of the parameter sample x from the class ensemble G i; The expression "defined as"; the parameter sample X is a certain group of data in x= (X 1,X2,X3,X4) in S21, and the grade probability refers to the probability of re-correction after the evaluation grade is obtained; rank probability= (likelihood x prior probability)/normalization constant.
S5: and (3) performing a return judgment test on the 30 groups of learning training samples by using the judging function formulas (4) and (5) of the three classification grades, wherein the calculated result is shown in the calculated evaluation grade of the table 2, and the evaluation grade calculated by the method is consistent with the evaluation grade calculated by the table 1.
Table 2 evaluation results
S6: solving the discrimination class of the evaluation grade of the test sample; according to equations (4) - (5), 10 sets of test samples were evaluated using the discriminant function of three evaluation grades, W 1,W2,W3. Taking sample 31 as an example, for x 31＝(95.35,89.71,66.75,87.85)T, according to the constructed discriminant function, we can find:
W1(x)＝2426.298
W2(x)＝2437.462
W3(x)＝2432.498
Comparing max { W 1(x),W2(x),W3(x),}＝W2 (x), so that the samples are classified into evaluation grade 2, and calculating to obtain each evaluation grade probability 0.00001,0.99345,0.00654 by a formula (5), wherein the parameter sample x in the formula (5) is 31, and the application analysis result of the test sample is shown in Table 3;
TABLE 3 application analysis results for test specimens
From the results shown in tables 2 and 3, the accuracy of the return judgment test by the method of the present invention was 100%, and the accuracy of the evaluation level of the asphalt pavement performance of the test sample was 100%.
,PQI＝wPCIPCI+wRQIRQI+wRDIRDI+wSRISRI,wPCI、wRQI、wRDI、wSRI In the existing specifications represent weights of the road surface damage condition index PCI, the road surface running quality index RQI, the road surface rut depth index RDI, the road surface anti-skid performance index SRI in the road surface use performance index PQI evaluation, respectively.
Table 4 entry index weight
The road surface use performance evaluation grade mentioned in S22 is classified into 3 categories, namely, the quality is more than or equal to 90, the quality is more than or equal to 80 and less than 90, the middle is less than 80, the road surface use performance evaluation grade is recorded as evaluation grades 1,2 and 3, the results of the conventional standard method are listed as the evaluation grades in the table 5, and the weight standard of the high-speed/first-grade road in the table 4 is adopted.
Table 5 results of calculations according to current specifications
/>
As can be seen from table 5, samples 4, 5, 15, 16, 18, 19, 22, 24, 25, 29, 35, 37 are inconsistent with the evaluation grades in table 1, and given the weights, the influence of the differences of the indexes on the weights is not considered, so that the road surface evaluation results are generally higher than the scores of experts after the actual field investigation, and are difficult to accurately adapt to all asphalt road surfaces, the service performance of the corresponding asphalt road surfaces cannot be quantitatively characterized, and the reliability of the evaluation results is not improved.
The method has the advantages that the region is wide, the difference between the south and the north is large, the climate (sunlight and rainfall) conditions, geological conditions, traffic volume, design and construction conditions of different roads in the same province are greatly different, each index (PCI, RQI, RDI, SRI) in the evaluation of the using performance of the asphalt pavement is the result of comprehensive influences of the climate, traffic, design, construction and the like, the difference is not considered by adopting a standard evaluation method, the difference of each index is obviously reflected, and the using performance of the pavement is difficult to evaluate accurately and scientifically. The invention establishes the discriminant function by relying on sample data, the sample data reflects the difference of influence of climate (sunshine and rainfall) conditions, geological conditions, traffic volume, design and construction conditions on the pavement performance, and the discriminant function and the grade probability calculation model established by the invention more emphasizes the difference of each index and the importance thereof, thereby greatly improving the accuracy, the scientificity and the rationality.
The foregoing description is only of the preferred embodiments of the present invention and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.
Claims (5)
1. The quantitative determination method for the service performance of the asphalt pavement is characterized by comprising the following steps of:
S1: collecting pavement service performance parameters: the road surface damage condition index PCI, the road surface running quality index RQI, the road rut depth index RDI and the road surface anti-skid performance index SRI are respectively marked as parameter samples X 1,X2,X3,X4, and the total parameter sample is X= (X 1,X2,X3,X4);
S2: determining prior probabilities q i of different performance evaluation grades according to the road surface use performance evaluation results corresponding to the known multiple groups of parameter samples, wherein the parameter samples corresponding to the road surface use performance evaluation grades, namely a classification overall G i;
s3: determining a discrimination function coefficient of the pavement using performance evaluation level, and constructing a discrimination function;
Wi(x)＝xTai+bi (1-1)
When (when) When x is G i; where a i represents a coefficient vector obtained from the parameter samples of G i, a i＝Σ-1μi;bi represents a constant term obtained from the parameter samples of G i,/>X T represents a transposed matrix of parameter sample X, which is a set of data of X in step S1, μ i represents a mean vector of G i, and G represents a class of evaluation level;
S4: determining the evaluation level of the use performance of other asphalt pavements by the constructed discriminant function and the evaluation level of the classified population G i by the constructed discriminant function;
s5: according to the basic principle of Bayes discrimination, calculating the grade probability that the parameter sample of the corresponding asphalt pavement in the step S4 belongs to the different classification populations G i according to the formula (1-2), and quantitatively representing the service performance of the corresponding asphalt pavement;
wherein: d (x, G i) represents the mahalanobis distance of the parameter sample x to the class ensemble G i;
Σ represents the covariance matrix of each classification ensemble G 1,G2,…Gi,…Gg.
2. The method for quantitatively determining the usability of an asphalt pavement according to claim 1, wherein in the step S2, the formula is represented by the following formulaThe prior probability q i of the classification ensemble G i is calculated, where n i represents the number of parameter samples corresponding to each evaluation level, i=1, 2.
3. The method for quantitatively determining the usability of asphalt pavement according to claim 1, wherein in the step S3, the average vector μ i of the classification population G i is expressed asCalculating; where x k (i) represents the kth sample value of the ith evaluation level,/>I=1, 2, … g, n i is the number of samples of the i-th evaluation level, which is the sample mean.
4. The method according to claim 1, wherein the step S5 further comprises, assuming that covariance matrices of the classification populations G 1,G2,…Gi,…Gg are equal, i.e., Σ 1＝Σ2＝Σi...＝Σg =Σ, estimating the classification populations G i, calculating according to the formula (1-3)An estimate of Σ;
wherein S 1,...,Sk,...,Sg is the standard deviation of the sample, X k (i) represents the kth sample value of the ith evaluation level; n i is the number of samples of the i-th evaluation level; /(I)Is the sample mean.
5. The method for quantitatively determining the usability of an asphalt pavement according to claim 1, further comprising: randomly sampling and arranging a plurality of times in a plurality of known parameter samples, taking one part of arranged samples as learning training samples and the other part of arranged samples as test samples; determining prior probabilities q i of different performance evaluation grades according to road surface use performance evaluation results corresponding to the learning samples, and classifying the overall G i, namely the learning samples corresponding to the road surface use performance evaluation grades; determining the road surface use performance evaluation grade of the test sample through the constructed discriminant function, determining the use performance evaluation grade of other asphalt road surfaces through the constructed discriminant function, determining the grade probability of the asphalt road surface parameter sample, and quantitatively representing the use performance of the corresponding asphalt road surface.
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