Abstract-After brief analysis of the current evaluation ways of the pavement performance, the integrated evaluation method of the pavement performance based on entropy weight radar chart theory is proposed in this study. In order to get objective, accurate evaluation results, after the analysis of radar chart theory and the improvement of the evaluation method of the traditional radar chart theory, a new evaluation method of the pavement performance based on entropy weight radar chart theory is built. Finally, by practical application, the reliability of this method is verified, which provides the reference and basis for evaluating pavement performance accurately.

Keywords-road engineering; pavement performance;

entropy weight radar chart theory; integrated evaluation; pavement preventive maintenance

I. INTRODUCTION

Transportation is the basis for the development of social economy and is also a powerful motive force of economic development and social improvement in China. 80s of last century, highways are achieved a breakthrough, and are entered the high-speed construction phase quickly in China. In the past 11 years, China's highways are increased from 652 kilometers to nearly 30,000 kilometers during 1992 to 2003. To the end of 2009, the mileage of China's highway has reached 65,000 kilometers. The total traffic mileage has become second in the world only next to the United States [1]. With the development of economic society, some new requirements of scientific road maintenance and from corrective to preventive road maintenance have been proposed by people [2]. Therefore, it has become an urgent problem to solve that pavement performance was assessed objectively and accurately.

At present, there are four chief assessment methods of pavement performance at home and abroad [3]: (1) Assessment method based on regression analysis model. It is based on a large amount of actual tested data and is scientific. However, simple regression analysis is difficult to express the complicated relationship between subjectivity and objectivity of pavement performance assessment. The relevance between assessment result and actual tested data is not very perfect, moreover, and this method is often restricted by the geography. (2) Systems analysis method is represented by Analytic Hierarchy

Process and Fuzzy Mathematics Method. Both have an analysis process with clear hierarchies and are very better in theory. Whereas, it is difficult to get an objective and just assessment of pavement performance because of the application of expert scores, serious man-caused effect and weak in objectivity in these two methods.(3) Comprehensive assessment about the grey theory. It is better in solving the problem of complex and fuzzy assessment index. Nevertheless, weighted functions, threshold value and grey classification coefficients are depended on the experience range of each index and also with some objectivity. (4) There are many other evaluation methods of pavement performance like grey theory method, for example, attribute theory method, neural network method and so on. The computation of attribute theory is more complicated, and the convergence of neural network method is slow because of itself deficiency, so model structure is difficult. Moreover, because of different functional forms and compact operators, it has different forms.

In view of the deficiency of above methods, a new method is proposed in this study, which makes use of the method of entropy weight to deal with measured data, combined with the method of chart expression and analysis- radar chart, and improving the deficiency in the process of quantification, then achieving the accurate and objective evaluation to pavement performance. The method is more intuitive, vivid, and is easy to operate and understand, and has reliable results of current integrated analysis method.

Ⅱ. THE THEORETICAL MODEL OF ENTROPY WEIGHT RADAR CHART

A. The theory of entropy weight radar chart The conception of entropy was derived from thermodynamics, in 1984, and American engineer C.E. Shannon lead entropy into the information theory. He defined the entropy of information source as:

i

n

ii ppCH ln

1∑

=

−= （1）

Where 0≥ip ，∑=

=n

iip

11 ， ）， n,2,1( =ipi

Pavement Performance Evaluation Based on Entropy Weight Radar Chart Theory

YAO Hongyun1, XING Rongjun2, XU Pai3 1School of Transportation Engineering, Chongqing Jiaotong University, Chongqing ,China

2School of Information Science and Engineering, Chongqing Jiaotong University, Chongqing ,China 3.School of Mechanical and Electrical Engineering, Chongqing Jiaotong University,Chongqing ,China

xingrong-12@163.com

978-1-4244-8503-1/10/$26.00 ©2010 IEEE 1791

denotes the probability of signal i in the information source; ipln− is the information value it brought; C denotes scale coefficient. The formula shows that the entropy and the probability have close relationship, and then it becomes the measurement of unsure degree of system state.

The radar chart is also called star graph, which is a kind of chart imitating radar fluorescent screen. Many variables are acted on a two dimension coordinate chart, leading rays from circle center according to variable weight coefficient. The length of the rays means the value of variable, connecting the extreme point of rays with lines, which makes a star [4-5], as Fig.1.

C1

C2

C3

Fig.1. Traditional radar chart

However, the theory of traditional radar chart is only applied with judging one evaluation object relative to others. It is difficult to compare with the comprehensive strength among objects in this method. Based on this, the integrated evaluation function is proposed in this study based on the theory of entropy weight radar chart. Furthermore, quantitative integrated evaluation is applied with evaluation object. B. The selection of evaluation index factors and modeling structure 1). The selection of evaluation index factors According to the principle of road engineering, for asphalt concrete pavement and cement concrete pavement, the four parameters are: pavement damage index PCI, running quality index RQI, rutting depth index RDI, anti-slide performance index SRI, which are main parameters reflecting performance and are also usual index when researching and evaluating the condition of pavement in China. Therefore, based on the measured data of some highway in Chong Qing, apply above four indexes for setting up pavement performance evaluation system. 2) Modeling procedure

Quantifying and synthesizing the inherent information of multi-object decision evaluation and the subjective information of decision-makers’ experience, then setting up the multi-object decision evaluation model based on the theory entropy weight radar chart, the modeling procedure is [6-8]:

(1) The numbers of sample(the numbers of lanes) is n, the evaluation index reflecting pavement performance is m, then, according to the measured data, the evaluation

index matrix X is built.

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

nmnn

m

m

ij

xxx

xxxxxx

X

21

22212

11211

（2）

Applying range standardization method for normalization [9];

)min()max()min(

jj

jijij xx

xxr

−−

= （3）

Where ijr denotes relative membership degree,

)max( jx 、 )min( jx denotes the maximum and the minimum of the index j. Getting the matrix after normalization ijR :

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

nmnn

m

m

ij

rrr

rrrrrr

R

21

22212

11211

（4）

(2) Computing the eigenvalue weigh of the evaluation index:

∑=

=m

jijijij rrp

1

/ （5）

Where m denotes the numbers of evaluation index. (3) Computing the entropy of the evaluation index j:

ij

n

iijj pp

me ln

ln1

1∑

=−= （6）

Where je denotes the entropy of the evaluation

index j, ijp denotes the eigenvalue weight, m denotes the numbers of index.

(4)Computing the weight of evaluation index j: The weight of evaluation index uses the difference

coefficient of the index for characterizing the importance of the index in the evaluation, the higher the value, the larger the contribution in the evaluation, vice versa.

∑=

−−=m

jjjj eew

1

)1(/)1( （7）

Weight vectors of evaluation index

are:T

mwwwww ),,,,( 321= , obviously, satisfying

the condition of normalization，that is, ∑=

=m

jjw

1

1 .

(5) The numbers of evaluation index is m: B1,B2,B3,……，Bm corroding to the axis in the radar chart, X1,X2,X3,……,Xm

(6) Index weight is in terms of the included angle of

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1792

index axis, as Fig.2: jwπθ 2j = （8）

Obviously: πθ 2j =∑

C1

C2

C3

1θ2θ

3θ

Fig.2. Improving radar chart

Obviously, when the numbers of evaluation index and the value of weight are fixed, as the order of index arrangement is non-unique, the area and perimeter are also non-unique. So some difficulties are brought into integrated evaluation. However, the average area and perimeter of all radar charts is unique, which is the solution to the above problem. Therefore, we compute the average area and perimeter of radar chart.

For the computation of the average area of radar chart, it is so easy to compute under the condition of rare index, but it is difficult to compute under the opposite condition. Therefore, firstly, we compute the average triangle area which is composed by two random indexes, then the average area of radar chart is m times of the average triangle area.

(7) The average area of radar chart:

Pm

m

k

m

hkhkihik

i

NNs 2

1

1

])sin(sin21[∑∑

−

= <

+=

θθ （9）

ii smS ⋅= ),,2,1( ni = （10）

Where iS denotes the average area of radar chart,

is denotes the triangle average area which is composed by two random indexes, m denotes the numbers of index.

In the same way, we can get the average perimeter of radar chart.

(8) The average perimeter of radar chart:

2

1

1

22 cos2

m

m

k

m

hkkihikihik

ki P

NNNNl

∑∑−

= <

−+=

θ (11)

2

1

1

22 cos2

m

m

k

m

hkhihikihik

hi P

NNNNl

∑∑−

= <

−+=

θ (12)

hiii lll += （13）

ii lmL ⋅= ),,2,1( ni = （14）

Where iL denotes the average perimeter of radar

chart, il denotes corresponding average length with

angle jθ of being composed by two random indexes. (9) Integrated evaluation function There are many methods of constructing function, in

general, getting the geometric mean of each evaluation vectors.

i

iiii L

SsS

vvfπ4

),(max

21 ×= （15）

Where ;max

1 sSv i

i =

22

24

)2( i

i

i

ii L

SL

Sv π

ππ==

mNms π2sin

22

maxmax ⋅= （16）

Smax denotes the area of N-regular-polygonal inscribed in the circle, and its radius is the maximum of radar chart axis. Nmax denotes the maximum of radar chart axis. m denotes the numbers of index.

Ⅲ. EXAMPLE APPLICATION

Now, take the measured data of some highway in Chong Qing for example to study the theory evaluation of entropy weight radar chart, the measured data of each road is as Tab. I.

Notes: the data derived from <highway partly road

asphalt paving maintenance 2009-2011 CCRDI-DS-8B203 short and medium project CCRDI-DS-8B203>

Getting the matrix of evaluation index:

TABLE I PERFORMANCE CONDITIONS OF PAVEMENT.

road

Pavement damage index

Running quality index

Rutting depth index

Anti-slide performance

index

PCI RQI RDI SRI

ascending passing 97.7 93.8 95.6 80.4

ascending main 95.3 92.3 95.5 88.0

descending passing 97.4 93.3 95.4 83.7

descending main 93.0 89.5 94.4 82.5

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1793

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

5.824.945.890.937.834.953.934.970.885.953.923.954.806.958.937.97

ijX

After normalization, getting normalized matrix:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

276316.0000434211.0833333.0883721.093617.0

1916667.0651163.0489326.00111

ijR

According to (7) and computing the weight of each index, as Tab. Ⅱ

According to（9）（10）（11）（12）（13）（14）computing the average area, the perimeter, as Tab. Ⅲ

According to (15), computing the integrated evaluation

function value of each evaluation objects, as TabⅣ

Though calculation analysis, according to national

current standard evaluation, the order of the four lanes is (notes : ”>” denotes the scores is high)

descending passing> ascending passing> ascending main> descending main

Notes: national current standard system< highway technical condition assessment standard JTG H20-2007>

However according to the evaluation method in this

study, the order of the four lanes is (notes: ”>” denotes the scores is high)

ascending main > descending passing > ascending passing > descending main

According to the evaluation method in this study, the results accord with national current standard results basically, the best road is ascending main lane. Obviously, the scores of the ascending main lane is highest, which because that the scores of each indexes of ascending main lane are all high, the indexes are balanced development. However, the former three indexes of ascending passing lane are all higher than that of ascending main lane, but the fourth index lower obviously, so the value of integrated evaluation is also lower. Comparing with the each index between descending passing lane and ascending passing lane, each index is balanced development, so ranking number two. However, the each index of descending main lane is also balanced development, but the value of each index is lower, that is the road condition is worst, so ranking number four.

Ⅳ CONCLUSION

(1) Comparing with the evaluation results of the

method proposed by this study and the national current method, both can reflect advantages and disadvantages of each lane. However, the balanced development of each evaluation index is well considered in this study, therefore, providing references for finding invisible disease on the road.

(2) Because that the results of the radar chart theory are vivid and intuitive, improving the deficiency of radar chart, a new attempt about entropy weight theory is lead into pavement performance comprehensive evaluation in this study.

(3) Taking the measured data of some highway for example in Chong Qing, making use of the theory of entropy weight radar chart, the objective weight of each evaluation index has been computed and comprehensive evaluation model has been built. Through computing and comparing with the situation of field test, the method is stable and reliable, having guiding significance for actual pavement performance evaluation.

(4) The comprehensive evaluation application results

TABLE Ⅱ WEIGHT TABLE OF EACH INDEX

PCI RQI RDI SRI

ej 0.737 0.760 0.780 0.463 wj 0.209 0.190 0.175 0.426 θj 1.312 1.196 1.098 2.678

TABLE Ⅲ THE AVERAGE AREA, THE AVERAGE PERIMETER OF THE RADAR

CHART

ascending

passing ascending

main descending

passing descending

main

iS 27613.6 27977.7 27891.2 26306.9

iL 976.07 987.8 982.97 955.63

maxs 19090.6 18240.5 18973.5 17822.7

TABLE Ⅳ

INTEGRATED EVALUATION RESULTS

ascending

passing ascending

main descending

passing descending

main

f 22.68 23.36 22.89 22.60

TABLE Ⅴ

NATIONAL CURRENT STANDARD EVALUATION

ascending

passing ascending

main descending

passing descending

main

PQI 93.8 93.4 94.1 90.7

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1794

of pavement performance entropy weight radar chart theory show that this method is an effective pavement performance comprehensive evaluation method next fuzzy evaluation and grey evaluation. The theory and algorithm is simple, the evaluation results are objective, vivid and intuitive, having strong practicality.

(5) Because that the time of entropy weight radar chart theory application is short, it has a lot of deficiency. For example, the choice of synthetic evaluation function is only simple geometric mean at the present stage, lacking of corresponding theoretical basis. Therefore, it still needs farther research and discussion to make it more perfect.

ACKNOWLEDGMENT Foundation item: Project (The Key Techniques and

Application for Energy Efficient and Emission Reduction warm asphalt mixtures) supported by Science and Technology Commission of Shanghai; Project (KJ080423) supported by National engineering research center for Highway Engineering in Mountainous Area; Project (CQMRCM-09-4) supported by Key Laboratory Open Foundation of Chongqing.

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[2] Tang Boming, Yao Zukang, Xia Ruilian, Song Sanyuan.

Long-Term Structural Performance Evaluation of Cement Concrete Pavement[J]. China Journal of Highway and Transport.1996,9(2):20-27

[3] Wang Zhaohui, Wang Xuancang, Ma Shibin. An Approximation Method of Interval Numbers for Comprehensive Evaluation of Pavement Performance[J]. Journal of Highway and Transportation Research and Development. 2009,26(1):21-25

[4] Dan Kaczynski, Leigh Wood and Ansie Harding. Using radar charts with qualitative evaluation: Techniques to assess change in blended learning. Active Learning in Higher Education 2008,9(1),23-41

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[6] Xu Song, Tang Boming, Zhu Hongzhou, He Zhaoyi. Analysis on Factors Influencing Moisture Stability of Bituminous Stabilized Macadam Based on Grey Correlation Entropy Method [J]. Journal of Chongqing Jiaotong University, 2007,27(6):1077-1080

[7] Zhang Shaokun, Fu Qiang, Zhang Shaodong. The Application of DRASCLP Model in Groundwater Vulnerability Evaluation Based on GIS and Entropy Weight.[J] Research of Soil and Water Conservation,2008,15(4):134-137

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[9] Zhang Baoxiang, Wan Li, Yu Cheng, Meng Fanhai. Fuzzy Optimization Assessment of DRASTIC Groundwater Vulnerability Based on Entropy Weight and GIS [J].Geoscience, 2009,23(1):150-156

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