Using Rough Set Theory to Induce Pavement ... - Semantic Scholar
Using Rough Set Theory to Induce Pavement Maintenance and Rehabilitation Strategy Jia-Ruey Chang1, Ching-Tsung Hung2, Gwo-Hshiung Tzeng3, and Shih-Chung Kang4 1
Department of Civil Engineering, MingHsin University of Science & Technology, No.1, Hsin-Hsing Road, Hsin-Fong, Hsin-Chu, 304, Taiwan [email protected] 2 Institute of Civil Engineering, National Central University, ChungLi, Taoyuan, 320, Taiwan [email protected] 3 Distinguished Chair Professor, Kainan University, No.1 Kainan Road, Luchu, Taoyuan County, 338, Taiwan [email protected] 4 Department of Civil Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan [email protected]
Abstract. Rough Set Theory (RST) is an induction based decision-making technique, which can extract useful information from attribute-value (decision) table. This study introduces RST into pavement management system (PMS) for maintenance and rehabilitation (M&R) strategy induction. An empirical study is conducted by using the pavement distress data collected from 7 county roads by experienced pavement engineers of Taiwan Highway Bureau (THB). For each road section, the severity and coverage of existing distresses and required M&R treatment were separately recorded. The analytical database consisting of 2,348 records (2,000 records for rule induction, and 348 records for rule testing) are established to induce M&R strategies. On the basis of the testing results, total accuracy and total coverage for the induced strategies are as high as 88.7% and 84.2% respectively, which illustrates that RST certainly can reduce distress types and remove redundant records to induce the proper M&R strategies. Keywords: Rough set theory (RST), Pavement management system (PMS), Maintenance and rehabilitation (M&R).
1
Introduction
Various distress types would occur to pavement because of dynamic loading, overweighed trucks, weak foundation, improper mix design, change of climates, etc [1]. Pavement distress survey records the severity and coverage of existing distress types in order to adopt proper maintenance and rehabilitation (M&R) treatments. It is extremely important that if proper M&R treatments can be implemented at right time for specific distress type. Proper M&R treatments can not only save long-term
expense but keep the pavement above an acceptable serviceability [2, 3]. However, M&R strategies are usually made by engineers’ subjective judgments. The objective of this study is to utilize Rough Set Theory (RST) in dealing with enormous distress data to induce proper M&R strategies for decreasing M&R judgment errors and improving the efficiency of decision-making process in pavement management system (PMS).
2
Rough Set Theory (RST)
In this section, the basic concept of RST is presented. Rough set, originally proposed by Pawlak [4], is a mathematical tool used to deal with vagueness or uncertainty. More detailed discussion about the process of RST can refer to the literatures [5-7]. The original concept of approximation space in rough set can be described as follows. Given an approximation space apr = (U , A ) , where U is the universe which is a finite and non-empty set, and A is the set of attributes. Then based on the approximation space, we can define the lower and upper approximations of a set. Let X be a subset of U , and the lower and upper approximation of X in A are conceptualized as Eq. (1) and (2), respectively. apr ( A ) = { x | x ∈ U , U / Ind ( A ) ⊂ X } .
(1)
apr ( A ) = { x | x ∈ U , U / Ind ( A) ∩ X ≠ ∅} .
(2)
where U / Ind ( A ) =
{( x , x ) ∈U ⋅U , f ( x , a ) = f ( x , a ) i
j
i
j
}.
∀a ∈ A
Eq. (1) represents the least composed set in A containing X , called the best lower approximation of X in A , and Eq. (2) represents the greatest composed set in A contained in X , called the best upper approximation. After constructing upper and lower approximations, the boundary can be represented as BN ( A ) = apr ( A ) − apr ( A ) .
(3)
According to the approximation space, we can calculate reducts and decision rules. Given an information system I = (U , A ) then the reduct, RED ( B ) , is a minimal set of attributes B ⊆ A such that rB (U ) = rA (U ) where
rB (U ) =
∑ card ( BX ) card (U )
i
.
(4)
denotes the quality of approximation of U by B . Once the reducts have been derived, overlaying the reducts on the information system can induce the decision rules. A decision rule can be expressed as ∅ ⇒ θ , where ∅ denotes the conjunction of elementary conditions, ⇒ denotes ‘indicates’, and θ denotes the disjunction of elementary decisions. The advantage of the induction based approaches such as RST is that it can provide the intelligible rules for decision-makers (DMs). These intelligible rules can help DMs to realize the contents of data sets. In the following empirical study, enormous records from pavement distress surveys are used to calculate reducts of distress types and to induce M&R strategies.
3
Empirical Study: Pavement M&R Strategy Induction
Although the development and implementation of M&R strategies for pavement is important, literature addressing this issue is limited. Colombrita et al. [8] build a multi-criteria decision model based on Dominance-based Rough Set Approach (DRSA) to provide highway agencies with a decision support system for more efficient M&R budget allocation. In the empirical study, 18 distress types and 4 M&R treatments provide as the attributes and decision variables, respectively. With the data collected from 2,348 asphalt-surfaced road sections, RST is employed to induce M&R strategies. Rough Set Exploration System (RSES) package is utilized to execute analyses [9, 10]. RSES is a software tool that provides the means for analysis of tabular data sets with use of various methods, in particular those based on RST. 3.1
Pavement Distress Survey and M&R treatments
Pavement distress survey is conducted for the purpose of monitoring the existing pavement condition and making the appropriate M&R decisions. Generally, the severity and coverage should be separately identified and recorded for each distress type on one road section. For accurate, consistent, and repeatable distress survey, one comprehensive distress survey manual is required for clarifying the definition, severity, and coverage of each distress type. In the empirical study, pavement distress survey was carried out following the Distress Identification Manual for the LongTerm Pavement Performance Program issued by Federal Highway Administration (FHWA) in June 2003 [11]. Furthermore, the required M&R treatment for each road section was decided according to the Standardized M&R Guidance which is issued by Taiwan Highway Bureau (THB) and used in various highway authorities in Taiwan. 3.2
Data Description
Pavement distress surveys were conducted on seven county roads with asphalt surface in Chung-Li Engineering Section of THB by 8 experienced pavement engineers. The seven county roads (110, 112, 112A, 113, 113A, 114 and 115) are located in northern
Taiwan. Engineers conducted surveys by walking or driving. The distress information and required M&R treatment for each road section were recorded. The totally collected 2,348 records (2,000 records are randomly selected for training dataset; the rest of 348 records are for testing dataset) are utilized in the empirical study, which are integrated as Table 1. The first column in Table 1 shows the record numbers, column 2 to column 19 illustrate the 18 distress types, and the last column refers to the required M&R treatment (decision variable). The details are described as follows: Table 1.
Summary of analytical database.
Rec. D1 1 2 2 1 3 2 4 2 5 2 6 1 7 1 8 2 9 1 10 1 11 2 12 4 13 5 14 2 15 1 : : : : 2345 0 2346 0 2347 0 2348 0
D2 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 : : 0 5 5 5
D3 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 : : 9 0 0 0
D4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : : 0 0 0 0
D5 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 : : 0 0 0 0
D6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : : 0 0 0 0
D7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 : : 0 0 0 0
D8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : : 0 0 0 0
D9 D10D11D12D13D14D15D16D17D18 M&R 0 0 0 0 0 0 0 5 0 0 1 0 0 0 0 0 6 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 : : : : : : : : : : : : : : : : : : : : : : 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4
• The empirical study explores 18 common distress types in Taiwan, which are represented from D1 to D18: D1. Alligator Cracking, D2. Block Cracking, D3. Longitudinal Cracking, D4. Transverse Cracking, D5. Edge Cracking, D6. Reflection Cracking, D7. Pothole, D8. Bleeding, D9. Rutting, D10. Corrugation, D11. Lane/Shoulder Drop-off, D12. Depression, D13. Structure Drop-off, D14. Utility Cut Patching, D15. Shoving, D16. Manhole Drop-off, D17. Patching Deterioration, D18. Raveling. Figure 1 shows examples of distress types. • The severity levels of distress are classified as L (low), M (moderate), and H (high). The coverage levels of distress are classified as A (local), B (medium), and C (extensive). Therefore, there are nine combinations (LA, LB, LC, MA, MB, MC, HA, HB, HC) of severity and coverage which are represented by number 1 to 9 respectively, and plus 0 represents no distress. For example, “D1 = 2” denotes Alligator Cracking occurs with low severity and medium coverage. Figure 2 shows examples of distress types with different severity and coverage combinations.
• M&R treatments for asphalt pavement used in the empirical study are classified as four types, which are represented as number 1 to 4 referring to no M&R required, localized M&R (such as full-depth patching, crack sealing, etc.), global M&R (such as fog seal, slurry seal, aggregate surface treatment, etc.), and major M&R (such as milling, hot recycling, heater scarifying, AC overlay, reconstruction, etc.) respectively. Figure 3 shows examples of M&R treatments.
D1. Alligator cracking
D3. Longitudinal cracking
D7. Pothole
D6. Reflection cracking
D11. Lane/shoulder drop-off
D14. Utility cut patching
Fig. 1. Examples of distress types.
(b)
(a)
Fig. 2. (a) Alligator cracking with high severity and extensive coverage (“D1 = 9”); (b) Patching with high severity and medium coverage (“D17 = 8”).
(a)
(b)
(c)
Fig. 3. M&R treatments: (a) Full-depth patching; (b) Hot recycling; (c) AC overlay.
3.3
Induction of M&R Strategies
First of all, reduct calculation is conducted using exhaustive algorithm [12] in RSES. Two reduct sets with 14 attributes each are obtained and shown below. The 13 attributes (cores) obtained from intersection of the two reduct sets are D1, D2, D3, D4, D5, D6, D7, D8, D10, D11, D13, D14, D16. It is found that D12. Depression, D17. Patching Deterioration and D18. Raveling are not shown in both reduct sets. • D1, D2, D3, D4, D5, D6, D7, D8, D9, D10, D11, D13, D14, D16 • D1, D2, D3, D4, D5, D6, D7, D8, D10, D11, D13, D14, D15, D16 Then, M&R strategies are induced based on the calculated reducts by randomly selecting 2,000 out of 2,348 records. The exhaustive algorithm [12] in RSES is chosen again to construct all minimal decision rules. Hence the induced 83 M&R strategies are shown in Table 2. For example, the first and second row in Table 2 represent the first and second M&R strategy, which match with 525 records (most records) and 315 records, respectively: • IF (D1=2) (That is, Alligator Cracking occurs with low severity and medium coverage.) THEN the required M&R treatment will be no M&R required (450 records) or localized M&R (75 records) • IF (D1=1) & (D5=1) (That is, both Alligator Cracking and Edge Cracking occur with low severity and local coverage.) THEN the required M&R treatment will be no M&R required (315 records) The exhaustive algorithm may be time-consuming due to computational complexity. Therefore approximate and heuristic solutions such as genetic or Johnson algorithms [12], which allow setting initial conditions for number of reducts to be calculated, required accuracy, coverage and so on, can be considered in the future. Table 2.
Summary of induced 83 M&R strategies.
No. of Rule (1-83) 1 2 3 4 5 : :
3.4
Match 525 315 210 192 176 : :
M&R Strategies (D1=2) => {M&R={1[450],2[75]}} (D1=1)&(D5=1) => {M&R=1[315]} (D1=1)&(D3=1) => {M&R={1[175],2[35]}} (D1=1)&(D3=1)&(D4=2) => {M&R={1[132],2[60]}} (D1=2)&(D5=1) => {M&R=1[176]} : :
Testing of M&R Strategies
The rest of 348 records are used to conduct testing analyses focusing on the induced 83 M&R strategies. The results are shown in Table 3 and discussed as follows. Note that 1, 2, 3, and 4 are represented as no M&R required, localized M&R, global M&R, and major M&R, respectively. Rows in Table 3 correspond to actual (required) 4 M&R treatments while columns represent decision values as returned by induced 83 M&R strategies (classifier).
Table 3.
Testing results of induced 83 M&R strategies.
Predicted Treatments 1 2 3 4 No. of obj. Accuracy 1 171 2 3 3 201 0.955 Actual 2 5 69 5 5 111 0.821 Treat. 3 2 3 15 3 27 0.652 4 0 1 1 5 9 0.714 True positive rate 0.961 0.920 0.625 0.313 Total number of tested objects: 348 Total accuracy: 0.887 Total coverage: 0.842
Coverage 0.891 0.757 0.852 0.778
• The values on diagonal represent correctly classified cases. If all non-zero values in Table 3 appear on the diagonal, we conclude that classifier makes no mistakes for the testing data. • Accuracy: Ratio of correctly classified objects from the class to the number of all objects assigned to the class by the classifier. For instance, 0.955 = 171/(171+2+3+3), 171 represents the number of records whose actual M&R treatment is 1 (no M&R required) as the same with the predicted M&R treatment by 83 M&R strategies. If the predicted treatment is 2 (2 records), 3 (3 records), and 4 (3 records), this must be incorrect. • Coverage: Ratio of classified (recognized by classifier) objects from the class to the number of all objects in the class. That is, for all M&R treatments, the ratio of strategies which can be recognized to carry out prediction (including incorrect prediction). For instance, 0.891 = (171+2+3+3)/201. • True positive rate: For each M&R treatment, the ratio of treatment which can be correctly predicted by 83 M&R strategies. For instance, 0.961 = 171/(171+5+2). • Total accuracy: Ratio of number of correctly classified cases (sum of values on diagonal) by 83 M&R strategies to the number of all tested cases. For instance, 0.887 = (171+69+15+5)/(171+2+3+3+5+69+5+5+2+3+15+3+1+1+5). • Total coverage: Total coverage equals 1 which means that all objects have been recognized (classified) by 83 M&R strategies. Such total coverage is not always the case, as the induced classifier may not be able to recognize previously unseen object. If some test objects remain unclassified, the total coverage value is less than 1. For instance, 0.842 = (171+2+3+3+5+69+5+5+2+3+15+3+1+1+5)/348. Note that total accuracy must be defined depending on the correct M&R treatment prediction. From the testing results, the total accuracy is as high as 0.887 and the total coverage is 0.842. Therefore, the 83 M&R strategies can be used to reliably reason M&R treatments in practice.
4
Conclusions
The purpose of pavement distress survey is to assist engineers in making proper M&R decisions. Proper M&R treatments can save long-term expense and keep the
pavement above an acceptable serviceability. However, M&R strategies are usually made by engineers’ subjective judgments. In the study, we have demonstrated the successful application of RST to the problem of inducing 83 M&R strategies by using 2,348 actual data (2,000 records for rule induction, and 348 records for rule testing). On the basis of the testing results, total accuracy and total coverage for the induced strategies is as high as 88.7% and 84.2% respectively, which illustrates that RST can easily reduce distress types and remove redundant records from enormous pavement distress data to induce proper M&R strategies. The induced M&R strategies can decrease M&R judgment errors and assist engineers to reliably reason M&R treatments. The efficiency of decision-making process in pavement management system (PMS) can be improved as well. The M&R strategies induced in this study provide a good foundation for further refinement when additional data is available. Acknowledgments. This study is partial results of project NSC 93-2211-E-159-003. The authors would like to express their appreciations to National Science Council of Taiwan for funding support.
References 1. Huang, Y.H.: Pavement Analysis and Design. Prentice Hall Inc. (1993) 2. Eltahan, A.A., Von Quintus, H.L.: LTPP Maintenance and Rehabilitation Data Review–Final Report. Publication No. FHWA-RD-01-019, Federal Highway Administration (FHWA) (2001) 3. Abaza, K.A., Ashur, S.A., Al-Khatib, I.A.: Integrated Pavement Management System with a Markovian Prediction Model. Journal of Transportation Engineering 130(1) (2004) 24–33 4. Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11(5) (1982) 341–356 5. Pawlak, Z., Grzymala-Busse, J., Slowinski, R., Ziarko, W.: Rough Sets. Communications of the ACM 38(11) (1995) 89–95 6. Grzymala-Busse, J.: Knowledge Acquisition under Uncertainty - A Rough Set Approach. Journal of intelligent and Robotic Systems 1(1) (1988) 3–16 7. Walczak, B., Massart, D.L.: Rough Sets Theory. Chemometrics and Intelligent Laboratory Systems 47(1) (1999) 1–16 8. Colombrita, R., Augeri, M.G., Lo Certo, A.L., Greco, S., Matarazzo, B., Lagana, G.: Development of a Multi-Criteria Decision Support System for Budget Allocation in Highway Maintenance Activities. Proceedings of Societa Italiana Infrastrutture Viarie (SIIV) 2004, Florence, Italy, Oct. 27-29 (2004) 9. Bazan, J.G., Szczuka, M.S.: The Rough Set Exploration System. In: Peters, J.F., Skowron, A. (eds.): Transactions on Rough Sets III. Lecture Notes in Computer Science, Vol. 3400. Springer-Verlag, Berlin Heidelberg New York (2005) 37–56 10.Rough Set Exploration System (RSES), Institute of Mathematics, Warsaw University (http://logic.mimuw.edu.pl/~rses) (2006) 11.Miller, J.S., Bellinger, W.Y.: Distress Identification Manual for the Long-Term Pavement Performance Program (FHWA-RD-03-031), Federal Highway Administration (2003) 12.Bazan, J.G., Nguyen, H.S., Nguyen, S.H., Synak, P., Wróblewski, J.: Rough Set Algorithms in Classification Problem. In: Polkowski, L., Tsumoto, S., Lin, T. (eds.): Rough Set Methods and Applications. Physica-Verlag, Heidelberg New York (2000) 49–88
Department of Civil Engineering, MingHsin University of Science & Technology, No.1, Hsin-Hsing Road, Hsin-Fong, Hsin-Chu, 304, Taiwan [email protected] 2 Institute of Civil Engineering, National Central University, ChungLi, Taoyuan, 320, Taiwan [email protected] 3 Distinguished Chair Professor, Kainan University, No.1 Kainan Road, Luchu, Taoyuan County, 338, Taiwan [email protected] 4 Department of Civil Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan [email protected]
Abstract. Rough Set Theory (RST) is an induction based decision-making technique, which can extract useful information from attribute-value (decision) table. This study introduces RST into pavement management system (PMS) for maintenance and rehabilitation (M&R) strategy induction. An empirical study is conducted by using the pavement distress data collected from 7 county roads by experienced pavement engineers of Taiwan Highway Bureau (THB). For each road section, the severity and coverage of existing distresses and required M&R treatment were separately recorded. The analytical database consisting of 2,348 records (2,000 records for rule induction, and 348 records for rule testing) are established to induce M&R strategies. On the basis of the testing results, total accuracy and total coverage for the induced strategies are as high as 88.7% and 84.2% respectively, which illustrates that RST certainly can reduce distress types and remove redundant records to induce the proper M&R strategies. Keywords: Rough set theory (RST), Pavement management system (PMS), Maintenance and rehabilitation (M&R).
1
Introduction
Various distress types would occur to pavement because of dynamic loading, overweighed trucks, weak foundation, improper mix design, change of climates, etc [1]. Pavement distress survey records the severity and coverage of existing distress types in order to adopt proper maintenance and rehabilitation (M&R) treatments. It is extremely important that if proper M&R treatments can be implemented at right time for specific distress type. Proper M&R treatments can not only save long-term
expense but keep the pavement above an acceptable serviceability [2, 3]. However, M&R strategies are usually made by engineers’ subjective judgments. The objective of this study is to utilize Rough Set Theory (RST) in dealing with enormous distress data to induce proper M&R strategies for decreasing M&R judgment errors and improving the efficiency of decision-making process in pavement management system (PMS).
2
Rough Set Theory (RST)
In this section, the basic concept of RST is presented. Rough set, originally proposed by Pawlak [4], is a mathematical tool used to deal with vagueness or uncertainty. More detailed discussion about the process of RST can refer to the literatures [5-7]. The original concept of approximation space in rough set can be described as follows. Given an approximation space apr = (U , A ) , where U is the universe which is a finite and non-empty set, and A is the set of attributes. Then based on the approximation space, we can define the lower and upper approximations of a set. Let X be a subset of U , and the lower and upper approximation of X in A are conceptualized as Eq. (1) and (2), respectively. apr ( A ) = { x | x ∈ U , U / Ind ( A ) ⊂ X } .
(1)
apr ( A ) = { x | x ∈ U , U / Ind ( A) ∩ X ≠ ∅} .
(2)
where U / Ind ( A ) =
{( x , x ) ∈U ⋅U , f ( x , a ) = f ( x , a ) i
j
i
j
}.
∀a ∈ A
Eq. (1) represents the least composed set in A containing X , called the best lower approximation of X in A , and Eq. (2) represents the greatest composed set in A contained in X , called the best upper approximation. After constructing upper and lower approximations, the boundary can be represented as BN ( A ) = apr ( A ) − apr ( A ) .
(3)
According to the approximation space, we can calculate reducts and decision rules. Given an information system I = (U , A ) then the reduct, RED ( B ) , is a minimal set of attributes B ⊆ A such that rB (U ) = rA (U ) where
rB (U ) =
∑ card ( BX ) card (U )
i
.
(4)
denotes the quality of approximation of U by B . Once the reducts have been derived, overlaying the reducts on the information system can induce the decision rules. A decision rule can be expressed as ∅ ⇒ θ , where ∅ denotes the conjunction of elementary conditions, ⇒ denotes ‘indicates’, and θ denotes the disjunction of elementary decisions. The advantage of the induction based approaches such as RST is that it can provide the intelligible rules for decision-makers (DMs). These intelligible rules can help DMs to realize the contents of data sets. In the following empirical study, enormous records from pavement distress surveys are used to calculate reducts of distress types and to induce M&R strategies.
3
Empirical Study: Pavement M&R Strategy Induction
Although the development and implementation of M&R strategies for pavement is important, literature addressing this issue is limited. Colombrita et al. [8] build a multi-criteria decision model based on Dominance-based Rough Set Approach (DRSA) to provide highway agencies with a decision support system for more efficient M&R budget allocation. In the empirical study, 18 distress types and 4 M&R treatments provide as the attributes and decision variables, respectively. With the data collected from 2,348 asphalt-surfaced road sections, RST is employed to induce M&R strategies. Rough Set Exploration System (RSES) package is utilized to execute analyses [9, 10]. RSES is a software tool that provides the means for analysis of tabular data sets with use of various methods, in particular those based on RST. 3.1
Pavement Distress Survey and M&R treatments
Pavement distress survey is conducted for the purpose of monitoring the existing pavement condition and making the appropriate M&R decisions. Generally, the severity and coverage should be separately identified and recorded for each distress type on one road section. For accurate, consistent, and repeatable distress survey, one comprehensive distress survey manual is required for clarifying the definition, severity, and coverage of each distress type. In the empirical study, pavement distress survey was carried out following the Distress Identification Manual for the LongTerm Pavement Performance Program issued by Federal Highway Administration (FHWA) in June 2003 [11]. Furthermore, the required M&R treatment for each road section was decided according to the Standardized M&R Guidance which is issued by Taiwan Highway Bureau (THB) and used in various highway authorities in Taiwan. 3.2
Data Description
Pavement distress surveys were conducted on seven county roads with asphalt surface in Chung-Li Engineering Section of THB by 8 experienced pavement engineers. The seven county roads (110, 112, 112A, 113, 113A, 114 and 115) are located in northern
Taiwan. Engineers conducted surveys by walking or driving. The distress information and required M&R treatment for each road section were recorded. The totally collected 2,348 records (2,000 records are randomly selected for training dataset; the rest of 348 records are for testing dataset) are utilized in the empirical study, which are integrated as Table 1. The first column in Table 1 shows the record numbers, column 2 to column 19 illustrate the 18 distress types, and the last column refers to the required M&R treatment (decision variable). The details are described as follows: Table 1.
Summary of analytical database.
Rec. D1 1 2 2 1 3 2 4 2 5 2 6 1 7 1 8 2 9 1 10 1 11 2 12 4 13 5 14 2 15 1 : : : : 2345 0 2346 0 2347 0 2348 0
D2 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 : : 0 5 5 5
D3 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 : : 9 0 0 0
D4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : : 0 0 0 0
D5 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 : : 0 0 0 0
D6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : : 0 0 0 0
D7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 : : 0 0 0 0
D8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : : 0 0 0 0
D9 D10D11D12D13D14D15D16D17D18 M&R 0 0 0 0 0 0 0 5 0 0 1 0 0 0 0 0 6 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 : : : : : : : : : : : : : : : : : : : : : : 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4
• The empirical study explores 18 common distress types in Taiwan, which are represented from D1 to D18: D1. Alligator Cracking, D2. Block Cracking, D3. Longitudinal Cracking, D4. Transverse Cracking, D5. Edge Cracking, D6. Reflection Cracking, D7. Pothole, D8. Bleeding, D9. Rutting, D10. Corrugation, D11. Lane/Shoulder Drop-off, D12. Depression, D13. Structure Drop-off, D14. Utility Cut Patching, D15. Shoving, D16. Manhole Drop-off, D17. Patching Deterioration, D18. Raveling. Figure 1 shows examples of distress types. • The severity levels of distress are classified as L (low), M (moderate), and H (high). The coverage levels of distress are classified as A (local), B (medium), and C (extensive). Therefore, there are nine combinations (LA, LB, LC, MA, MB, MC, HA, HB, HC) of severity and coverage which are represented by number 1 to 9 respectively, and plus 0 represents no distress. For example, “D1 = 2” denotes Alligator Cracking occurs with low severity and medium coverage. Figure 2 shows examples of distress types with different severity and coverage combinations.
• M&R treatments for asphalt pavement used in the empirical study are classified as four types, which are represented as number 1 to 4 referring to no M&R required, localized M&R (such as full-depth patching, crack sealing, etc.), global M&R (such as fog seal, slurry seal, aggregate surface treatment, etc.), and major M&R (such as milling, hot recycling, heater scarifying, AC overlay, reconstruction, etc.) respectively. Figure 3 shows examples of M&R treatments.
D1. Alligator cracking
D3. Longitudinal cracking
D7. Pothole
D6. Reflection cracking
D11. Lane/shoulder drop-off
D14. Utility cut patching
Fig. 1. Examples of distress types.
(b)
(a)
Fig. 2. (a) Alligator cracking with high severity and extensive coverage (“D1 = 9”); (b) Patching with high severity and medium coverage (“D17 = 8”).
(a)
(b)
(c)
Fig. 3. M&R treatments: (a) Full-depth patching; (b) Hot recycling; (c) AC overlay.
3.3
Induction of M&R Strategies
First of all, reduct calculation is conducted using exhaustive algorithm [12] in RSES. Two reduct sets with 14 attributes each are obtained and shown below. The 13 attributes (cores) obtained from intersection of the two reduct sets are D1, D2, D3, D4, D5, D6, D7, D8, D10, D11, D13, D14, D16. It is found that D12. Depression, D17. Patching Deterioration and D18. Raveling are not shown in both reduct sets. • D1, D2, D3, D4, D5, D6, D7, D8, D9, D10, D11, D13, D14, D16 • D1, D2, D3, D4, D5, D6, D7, D8, D10, D11, D13, D14, D15, D16 Then, M&R strategies are induced based on the calculated reducts by randomly selecting 2,000 out of 2,348 records. The exhaustive algorithm [12] in RSES is chosen again to construct all minimal decision rules. Hence the induced 83 M&R strategies are shown in Table 2. For example, the first and second row in Table 2 represent the first and second M&R strategy, which match with 525 records (most records) and 315 records, respectively: • IF (D1=2) (That is, Alligator Cracking occurs with low severity and medium coverage.) THEN the required M&R treatment will be no M&R required (450 records) or localized M&R (75 records) • IF (D1=1) & (D5=1) (That is, both Alligator Cracking and Edge Cracking occur with low severity and local coverage.) THEN the required M&R treatment will be no M&R required (315 records) The exhaustive algorithm may be time-consuming due to computational complexity. Therefore approximate and heuristic solutions such as genetic or Johnson algorithms [12], which allow setting initial conditions for number of reducts to be calculated, required accuracy, coverage and so on, can be considered in the future. Table 2.
Summary of induced 83 M&R strategies.
No. of Rule (1-83) 1 2 3 4 5 : :
3.4
Match 525 315 210 192 176 : :
M&R Strategies (D1=2) => {M&R={1[450],2[75]}} (D1=1)&(D5=1) => {M&R=1[315]} (D1=1)&(D3=1) => {M&R={1[175],2[35]}} (D1=1)&(D3=1)&(D4=2) => {M&R={1[132],2[60]}} (D1=2)&(D5=1) => {M&R=1[176]} : :
Testing of M&R Strategies
The rest of 348 records are used to conduct testing analyses focusing on the induced 83 M&R strategies. The results are shown in Table 3 and discussed as follows. Note that 1, 2, 3, and 4 are represented as no M&R required, localized M&R, global M&R, and major M&R, respectively. Rows in Table 3 correspond to actual (required) 4 M&R treatments while columns represent decision values as returned by induced 83 M&R strategies (classifier).
Table 3.
Testing results of induced 83 M&R strategies.
Predicted Treatments 1 2 3 4 No. of obj. Accuracy 1 171 2 3 3 201 0.955 Actual 2 5 69 5 5 111 0.821 Treat. 3 2 3 15 3 27 0.652 4 0 1 1 5 9 0.714 True positive rate 0.961 0.920 0.625 0.313 Total number of tested objects: 348 Total accuracy: 0.887 Total coverage: 0.842
Coverage 0.891 0.757 0.852 0.778
• The values on diagonal represent correctly classified cases. If all non-zero values in Table 3 appear on the diagonal, we conclude that classifier makes no mistakes for the testing data. • Accuracy: Ratio of correctly classified objects from the class to the number of all objects assigned to the class by the classifier. For instance, 0.955 = 171/(171+2+3+3), 171 represents the number of records whose actual M&R treatment is 1 (no M&R required) as the same with the predicted M&R treatment by 83 M&R strategies. If the predicted treatment is 2 (2 records), 3 (3 records), and 4 (3 records), this must be incorrect. • Coverage: Ratio of classified (recognized by classifier) objects from the class to the number of all objects in the class. That is, for all M&R treatments, the ratio of strategies which can be recognized to carry out prediction (including incorrect prediction). For instance, 0.891 = (171+2+3+3)/201. • True positive rate: For each M&R treatment, the ratio of treatment which can be correctly predicted by 83 M&R strategies. For instance, 0.961 = 171/(171+5+2). • Total accuracy: Ratio of number of correctly classified cases (sum of values on diagonal) by 83 M&R strategies to the number of all tested cases. For instance, 0.887 = (171+69+15+5)/(171+2+3+3+5+69+5+5+2+3+15+3+1+1+5). • Total coverage: Total coverage equals 1 which means that all objects have been recognized (classified) by 83 M&R strategies. Such total coverage is not always the case, as the induced classifier may not be able to recognize previously unseen object. If some test objects remain unclassified, the total coverage value is less than 1. For instance, 0.842 = (171+2+3+3+5+69+5+5+2+3+15+3+1+1+5)/348. Note that total accuracy must be defined depending on the correct M&R treatment prediction. From the testing results, the total accuracy is as high as 0.887 and the total coverage is 0.842. Therefore, the 83 M&R strategies can be used to reliably reason M&R treatments in practice.
4
Conclusions
The purpose of pavement distress survey is to assist engineers in making proper M&R decisions. Proper M&R treatments can save long-term expense and keep the
pavement above an acceptable serviceability. However, M&R strategies are usually made by engineers’ subjective judgments. In the study, we have demonstrated the successful application of RST to the problem of inducing 83 M&R strategies by using 2,348 actual data (2,000 records for rule induction, and 348 records for rule testing). On the basis of the testing results, total accuracy and total coverage for the induced strategies is as high as 88.7% and 84.2% respectively, which illustrates that RST can easily reduce distress types and remove redundant records from enormous pavement distress data to induce proper M&R strategies. The induced M&R strategies can decrease M&R judgment errors and assist engineers to reliably reason M&R treatments. The efficiency of decision-making process in pavement management system (PMS) can be improved as well. The M&R strategies induced in this study provide a good foundation for further refinement when additional data is available. Acknowledgments. This study is partial results of project NSC 93-2211-E-159-003. The authors would like to express their appreciations to National Science Council of Taiwan for funding support.
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