Research Article  Open Access
Hui Wang, Haoqi Tan, Tian Qu, Jiupeng Zhang, "Effects of Test Conditions on APA Rutting and Prediction Modeling for Asphalt Mixtures", Advances in Materials Science and Engineering, vol. 2017, Article ID 2062758, 11 pages, 2017. https://doi.org/10.1155/2017/2062758
Effects of Test Conditions on APA Rutting and Prediction Modeling for Asphalt Mixtures
Abstract
APA rutting tests were conducted for six kinds of asphalt mixtures under airdry and immersing conditions. The influences of test conditions, including load, temperature, air voids, and moisture, on APA rutting depth were analyzed by using grey correlation method, and the APA rutting depth prediction model was established. Results show that the modified asphalt mixtures have bigger rutting depth ratios of airdry to immersing conditions, indicating that the modified asphalt mixtures have better antirutting properties and water stability than the matrix asphalt mixtures. The grey correlation degrees of temperature, load, air void, and immersing conditions on APA rutting depth decrease successively, which means that temperature is the most significant influencing factor. The proposed indoor APA rutting prediction model has good prediction accuracy, and the correlation coefficient between the predicted and the measured rutting depths is 96.3%.
1. Introduction
Rutting prevention has become one of the most indemand topics of study with moreextensive research on damage to asphalt pavement. Studies all over the world have established a variety of rutting test methods to analyze and evaluate the antirutting properties of asphalt mixtures. APA (Asphalt Pavement Analyzer) rutting test has gained much international attention in recent years for such advantages as the ability to simulate live load conditions. In 2001, NCAT (National Center for Asphalt Technology) evaluated the applicability of various methods for evaluating the antirutting performance, including APA, HWTD (Hamburg Wheeltracking Device), FRT (French Pavement Rutting Tester), RLWT, and triaxial repeated load creep tests, and preferentially recommended APA rutting test. Subsequently, numbers of research have conducted the antirutting properties of asphalt mixtures by using APA test.
Xie et al. researched moisture susceptibility through APA and analyzed the results of watersubmerged rut testing, from which they presented an index of water submergence stability to assess water resistance of different asphalt mixtures [1]. Han et al. investigated the effects of water on permanent deformation potential by using APA and indicated that APA testing form, preconditioning conditions, and the freezing and thawing cycle times are the main universal reasons that cause a greater extent of deformation in wet rut compared with dry rut [2]. Zhang et al. presented a rule of the effect of different size aggregates on the hightemperature performance of asphalt mixtures on the basis of APA tests and indicated a reasonable percentage of different size aggregates, which could help to design both skeleton and denseconstruction asphalt mixtures [3]. Junbiao et al. used digital imageprocessing to analyze the loading modes of the RLWT (Rotary Loaded Wheel Tester) and APA rutting tests, by comparing the angle between the long axis and the axis of coarse aggregates in RLWT testing specimens, APA testing specimens, and untested specimens; they found that the loading modes of RLWT and APA rutting tests differ notably [4]. Cao et al. studied the deformation property of asphalt mixtures at constant and varying temperatures through APA and determined that deformation curves have two phases: delayed elastic deformation and viscous deformation [5]. Xue et al. performed APA tests on SAWI (StressAbsorbing Waterproof Interlayers) to analyze the fatigue properties and indicated that the fatigue life of SAWI is 3.32 times that of common asphalt concrete [6]. Xiao et al. researched the compaction properties of different asphalt mixtures and analyzed their abilities to resist rutting and water damage by using APA [7, 8]. Rushing and Little assessed rutting sensitivity through APA, triaxial static creep, and triaxial repeated load creep tests and found that the increasing rate of permanent strain and the flow time value determined via triaxial static creep tests has the strongest correlation to APA rutting depth [9]. Ali et al. assessed antirutting properties of WMA (Warm Mix Asphalt) by using APA, pointing out that reducing the production temperature of foamed WMA might result in the increasing potential of permanent deformation and moistureinduced damage [10]. Xie and Shen researched the rutting resistance, moisture susceptibility, and fatigue resistance of rubberized SMA (Stone Matrix Asphalt), analyzing the incorporation of CRM (Crumb Rubber Modifier) by using APA [11]. Malladi et al. researched moisture and rutting susceptibility of WMA by using APA and indicated that WMA performance is on a par with that of HMA and good potential for the widespread use of WMA [12].
Numbers of achievements have been obtained on APA test in the last decades, and most of the previous research focused on the evaluation of asphalt mixture antirutting performance by using APA test. Few attempts have reported the effects of testing conditions on APA rutting depth and are not sufficient in understanding the results of APA rutting tests influenced by test conditions. Therefore, in this paper, the APA experiments were performed under different test conditions for further understanding the influences of load, temperature, and other conditions on rutting depth, and an APA rutting prediction model was established to provide reference for further popularization and application of APA rutting tests.
2. Experimental Design
2.1. Asphalt Mixture Design and Specimen Preparation
Four kinds of AC20 (Asphalt Concrete whose nominal maximum size of aggregate is 20 mm) asphalt mixtures and two kinds of AC13 (Asphalt Concrete whose nominal maximum size of aggregate is 13 mm) asphalt mixtures (namely, AC20 coarsetype modified asphalt, AC20 coarsetype matrix asphalt, AC20 finetype modified asphalt, AC20 finetype matrix asphalt, AC13 modified asphalt, and AC13 matrix asphalt) were designed according to highway project to research the influence of experimental conditions on APA rutting tests. Shell 70 matrix asphalt and SBS modified asphalt were used in the experiments. Their technical properties are given in Table 1, and Table 2 conforms to the technical requirements published in Technical Specification for Construction of Highway Asphalt Pavement (JTG F402004).


Three kinds of aggregate gradations (namely, AC20 coarsetype, AC20 fine type, and AC13) were selected to mix with two kinds of asphalt binders, respectively, to prepare six kinds of asphalt mixtures. Optimal asphalt contents of asphalt mixtures were determined by the Marshall method; the results are presented in Table 3.

Cylinder specimens ( 150 × 75 mm) were molded by using SGC (Superpave Gyratory Compactor) according to the results of the material composition designs given previously, and the target air voids were 4 and 7%.
2.2. APA Rutting Test Schemes
APA rutting tests using SGC cylinder specimens (as shown in Figure 1) were conducted in both dry and immersion conditions, respectively. Under dry conditions, the specimens with 4% air voids were selected for APA rutting tests, and the test temperatures were 40, 50, and 60°C. The APA rutting test was the force of a concave wheel applied indirectly on the specimen through an inflatable rubber hose. In this paper, standard load was N; standard air pressure of the rubber hose was kPa; and running frequency of the wheel was 60 Hz, that is, 60 times back and forth per minute. To analyze the effect of overloading on APA rutting, two combinations of load and tire pressure (533 N/827 kPa and 889 N/827 kPa) were increased to test at 60°C.
Under immersion conditions, the specimens with the air voids of 4 and 7% were tested, respectively; test temperatures were 50 and 60°C, respectively; load was 445 N; and tire pressure was 690 kPa. All the specimens were placed in APA test machines at the test temperature for 6–24 h before testing to ensure that the specimens would reach the test temperature and maintain temperature equalizing.
3. Results and Discussion
3.1. Influence of Temperature on APA Rutting under Dry Conditions
Under dry conditions, the APA rutting depth development trends for different types of asphalt mixtures under three different temperatures are shown in Figures 2–4. Results show the hightemperature performances of the asphalt mixtures according to rutting depthsize order, under three different temperatures reaching unanimity, namely, AC20 finetype matrix asphalt mixture > AC13 matrix asphalt mixture > AC20 coarsetype matrix asphalt mixture > AC20 finetype modified asphalt mixture > AC13 modified asphalt mixture > AC20 coarsetype modified asphalt mixture. Thus, it shows that modified bitumen can improve the hightemperature performance of asphalt mixtures. At a test temperature of 40°C, the growth of rutting of different asphalt mixtures is moderate with small degree rutting. At 50°C, rutting is 23 times bigger than rutting at 40°C; rutting at 60°C is approximately 1.5 times bigger than rutting at 50°C and 3–5 times bigger than rutting at 40°C. Comparisons of APA rutting test results indicate that temperature appears to significantly affect the development of rutting, which has been confirmed by Zhang et al. [13–15].
Results show that rutting depth changes with the number of loads and the temperature, according to the APA rutting test results under different temperatures. Thus, the temperatureeffects regression model shown in (1) was established.where is the predicted rutting depth (mm); is the benchmark rutting depth under temperature and at loading times on the basis of the rutting test (mm); are the test temperature and the loading times corresponding to the predicted rutting depth; and are the regression coefficients of the materials.
For the asphalt mixtures, many factors, such as asphalt properties, asphalt content, air void, aggregate gradation, and others could influence rutting depth and the performance coefficient of the materials . The model would be greatly complicated if these factors were considered in the temperatureeffects regression model of rutting depth. Therefore, to simplify the model, is introduced into formula (1) to standardize the influence of the asphalt mixture type for predicting rutting depth. Benchmark rutting depth is the result of the APA rutting test under various conditions of temperature and loading times . Groups of data (324) from 54 times rutting tests were used in the regression analysis. Eight benchmark depths were selected to regress, respectively, and each of them corresponded to different test temperatures and loading times. The regression analyses show the following: a correlation coefficient of , high correlations exist between both the independent and the dependent variables; standard error ≤ 0.2 mm, the fitting degree of regression equation is good; and significance , the established regression equation is very significant. The average values and were applied in the regression equation because a negligible difference exists between the regression coefficients obtained from the eight benchmark depths. Thus, (2) can be obtained.
3.2. Influence of Load on APA Rutting under Dry Conditions
Under dry conditions, the influence from combinations of different loads and tire pressures on the APA rutting depth of asphalt mixtures is shown in Figure 5. The results show that the orders of asphalt mixtures under three combinations of load and tire pressure (namely, 690 kPa/445 N, 827 kPa/533 N, and 827 kPa/889 N) are the same, from excellent to poor for AC20 coarsetype modified asphalt, AC13 modified asphalt, AC20 finetype modified asphalt, AC20 coarsetype matrix asphalt, AC13 matrix asphalt, and AC20 finetype matrix asphalt, respectively.
(a) Matrix asphalt mixture
(b) Modified asphalt mixture
The testing results are consistent with research results of Gu et al., which indicate rutting depths all tend to increase with increases in load and tire pressure [16, 17]. Little difference exists among rutting test results under combinations of 690 kPa/445 N and 827 kPa/533 N; rutting depths under combinations of 827 kPa/533 N were approximately 1.08 times that of the rutting depths under combinations of 690 kPa/445 N. Comparing combinations of 690 kPa/445 N revealed that the load of 827 kPa/533 N increased 20% and tire pressure increased 20%, however, tire ground pressure increased by only 6%, that is, 42 kPa. A large difference exists between the rutting test results under combinations of 827 kPa/889 N and two other combinations. For matrix asphalt mixtures, rutting deeper than 12 mm appeared under far fewer than 8000 load times. For modified asphalt mixtures, the rutting depths under combinations of 827 kPa/889 N were approximately 2.72 times that of rutting depths under combinations of 690 kPa/445 N and approximately 2.45 times that of rutting depths under combinations of 827 kPa/533 N. Thus, overloading requires more attention for its significant effect on the rutting depth of asphalt mixtures.
3.3. Development Trend of Immersion APA Rutting
Development trends of APA rutting depth of asphalt mixtures with the air voids of 4% and 7% under different temperature and humidity conditions are shown in Figures 6–9. Cracking, asphalt exfoliating, and stripping appeared at the interface of aggregate and asphalt under the water bath condition in the APA rutting test. A decline in the adhesion of aggregate and asphalt also results in the reduction of the structural stability of the asphalt mixture. The larger rutting appeared under the drier conditions in the APA rutting test.
The rutting depth ratio is defined as the ratio of dry rutting depth and immersion rutting depth, and the water stability of asphalt mixture with greater rutting ratio is better [18]. The rutting depth ratios were calculated according to APA rutting depths under different immersing conditions, and the results are shown in Figures 10–13.
(a) Matrix asphalt mixture
(b) Modified asphalt mixture
(a) Matrix asphalt mixture
(b) Modified asphalt mixture
(a) Matrix asphalt mixture
(b) Modified asphalt mixture
(a) Matrix asphalt
(b) Modified asphalt
Analyses show that the rutting depth ratio of the modified asphalt mixture is greater which means that the water stability is better considering the viscosity of modified asphalt is greater than that of matrix asphalt, more polar materials exist in the matrix asphalt, and the matrix asphalt has good wettability. The water stabilities of the AC13 modified asphalt mixture and the AC13 matrix asphalt mixture are worse than those of the other limestone mixtures because of the use of acidic stone granite. The AC13 matrix asphalt mixture is obvious, its rutting depth ratio is the smallest, and the specimens were spilled at the test temperature of 60°C.
Comparisons of the rutting depth ratios at different loading times show that the rutting depth ratios increases, whereas the influence of water decreases gradually with the increase in loading times. The air void of asphalt mixtures decreases and the aggregate skeleton resistance increases with the repeated action of the loading wheel. The increasing amplitude of porewater pressure is smaller compared to that of the increasing amplitude of the aggregate skeleton resistance, although porewater pressure also increases. Thus, the influence of water decreases gradually. The results also show that the order of the water stability of the asphalt mixture ordered by rutting depth ratios under 25 or by 4000 loading times is not stable, whereas the order of the water stability of the asphalt mixture ordered by rutting depth ratios under 8000 loading times is more stable. Therefore, 8000 loading times of APA equipment should be ensured when evaluating tests of water stability performance, and test results from loading times under 25 or 4000 are not recommended for evaluating water stability of asphalt mixtures.
3.4. Grey Correlation Analyses of Influencing Factors in APA Rutting Tests
Numbers of researchers analyzed influencing factors of rutting deformation characteristics on asphalt pavement. Peilong et al. analyzed the correlation of influencing factors of rut resistance using grey theory, indicating that rut deformation rate has the maximum grey correlation with rate rut depth among five influencing factors of void ratio, graduation index, rut deformation rate, passing rate at 4.75 mm in middle layer, and filler/asphalt ration [19]. But few attempts have been reported about effects of test conditions on APA rutting using grey theory. Therefore, the correlation degrees of temperature, combinations of load and tire pressure, and water on APA rutting depths were researched by using the grey correlation method on the basis of the tests described previously [20]. The grey correlation method orders correlation degrees and identify the main factor influencing the target value by calculating their target values and influence factors.
Firstly, pinpoint both the reference sequence and the compared sequence when using the grey correlation method for analysis. Assume that the reference sequence is , ; the comparison sequence is , . Establish an average value for each of these sequences; namely, each sequence is divided by the average value, and a new sequence is obtained.In (3), .In (4), .
is new reference sequence; is a new compared sequence. The correlation of the reference curve and the compared curve at time (indicator and space) isIn (5), is the distinguish coefficient; its value is between 0 and 1; is the smallest difference between two poles; is the biggest difference between two poles; ; .
The expression of the correlation degree is ; is the correlation degree of the curve and the reference sequence . When the correlation degrees are ordered, the results show that the bigger leads to the steadier development trend of and and the greater influence of on . The calculation results of the grey correlation degree of different factors are shown in Figure 14. The Abscissas 1 to 6 corresponded to the AC20 coarsetype matrix asphalt mixture, AC20 coarsetype modified asphalt mixture, AC20 finetype matrix asphalt mixture, AC20 finetype modified asphalt mixture, AC13 matrix asphalt mixture, and the AC13 modified asphalt mixture.
The results show that the order of correlation degree is temperature, load, air void, and immersing condition. Thus, temperature is the closest correlation associated with asphalt mixture rutting depth. The main reason is that the asphalt binder in the asphalt mixture is temperaturesensitive, and the deformation depends significantly on temperature. Under hightemperature conditions, the asphalt is prone to flow, and rutting appears. This finding also verifies that asphalt pavement rutting forms mainly under high temperatures. Also, load is closely associated with asphalt mixture rutting depth. Increasing the load might damage the interlock structure between the aggregates in the asphalt mixture, which might affect the temperature of the pavement structure and lead to rutting. The relationship between air void and rutting is that the existence of air voids might cause supplementary compaction under loading. However, the air voids of asphalt mixtures are limited. Hence, the correlation degree of air voids is relatively low. Meanwhile, rutting should be weak. Water damage to the asphalt mixture is mainly attributable to water entering the interface of the asphalt and the aggregate and causing asphalt and aggregate spalling. However, mixtures with dense gradation are mainly used in this research while the water that could enter the interface of the asphalt to aggregate is limited. Thus, water has a relatively low influence on the stability of mixtures.
4. Indoor Rutting Prediction Modeling and Validation Based on APA
With reference to the model of APA rutting depthtemperatureloading times in formula (1), the indoor APA rutting prediction model accounts for many factors such as temperature, loading time, loading level, and air void and presents these factors in where , , , are the benchmark parameters of the indoor APA rutting prediction model and is the benchmark parameter showing the characterization of resistance to the permanent deformation of the material, which is obtained from the APA rutting depth under specific conditions. The specific conditions are that the test temperature is the reference temperature ; the test loading time is the reference loading time ; the test loading level is the reference loading level ; and the test air void is the reference air void .
The APA standard test conditions are as follows: °C; times; MPa; and . The data set (, , , , and ) could be obtained from the rutting depth under other test conditions divided by the rutting depth under standard test conditions and other test conditions divided by the standard test conditions. By taking the logarithm of each data in the data set, is the dependent variable, while , , , and are the independent variables. The regression index could be obtained after multiple regression analyses of the data set. By applying these results to (6), an APA rutting prediction model which could take into consideration any significant factors could be obtained.
According to the predicted APA rutting depth in (7), the correlation coefficient of the predicted and measured APA rutting depths shown in the Figure 15 reaches 96.3%. Only seven data deviations exist, which are more than 1 mm among the measured and the predicted APA rutting depths in 1188 groups of experimental data. The biggest deviation is 2.392 mm.
5. Conclusions
(1)The orders of rutting depths for 6 kinds of asphalt mixtures under different temperatures and combinations of load and tire pressure are almost the same; that is, AC20 type matrix asphalt mixture > AC13 matrix asphalt mixture > AC20 coarsetype matrix asphalt mixture > AC20 finetype modified asphalt mixture > AC13 modified asphalt mixture > AC20 coarsetype modified asphalt mixture. Compared with the matrix asphalt mixture, the APA rutting depth of the modified asphalt mixture is smaller. Besides he rutting resistance of the modified asphalt mixture is also better.(2)The effect of temperature on the development of rutting is nonnegligible. At a test temperature of 40°C, the development of rutting of different asphalt mixtures is relatively mild, and the rutting depth is small. Rutting depth at a test temperature of 50°C is 2 to 3 times as big as the rutting at 40°C, whereas rutting depth at 60°C is approximately 1.5 times as large as rutting at 50°C. The regression model of APA rutting depthtemperatureloading times was established and verified on the basis of rutting depth under different test temperatures and loading times.(3)The correlation degrees of temperature, combinations of load and tire pressure, and water on the APA rutting depth were researched through grey correlation method. The results show that temperature is the most significant influencing factor.(4)The indoor APA rutting prediction model considering several factors such as temperature, loading times, loading level, and air void was established. The prediction of this model is precise and convincing. Rutting depth under other conditions could be predicted on the basis of APA rutting depth under these benchmark conditions.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (no. 51408043), the Department of Science & Technology of Shaanxi Province (no. 2016KJXX69), the Open Foundation of Key Laboratory of Highway Construction & Maintenance Technology in Loess Region, Ministry of Transport, China (KLTLRY117), and the Special Fund for Basic Scientific Research of Central College of Chang’an University (nos. 310821153502 and 310821173501). The authors gratefully acknowledge their financial support.
References
 J. Xie, Y.Z. Li, and L.G. Shao, “Laboratory evaluation on the moisture susceptibility of hot asphalt mixtures by asphalt pavement analyzer,” Journal of Hunan University of Science and Technology (Natural Science Edition), vol. 20, no. 2, pp. 53–57, 2005. View at: Google Scholar
 H.F. Han, W.M. Lu, and G.P. He, “Effects of water on permanent deformation potential of hotmix asphalt,” China Journal of Highway and Transport, vol. 16, no. 4, pp. 4–8, 2003. View at: Google Scholar
 C. Zhang, Z. Xu, R. Yang, and Y. Qiu, “High temperature performance and gradation design in skeleton and dense construction asphalt mixture,” Journal of Tongji University, vol. 36, no. 5, pp. 603–608, 2008. View at: Google Scholar
 Z. Junbiao, X. Ke, and Z. Xiaoning, “Comparative analysis of loading mode between RLWT and APA rutting test,” Journal of Highway and Transportation Research and Development, vol. 7, pp. 331–336, 2006. View at: Google Scholar
 L.P. Cao, L.J. Sun, and Z.J. Dong, “Deformation property of asphalt mixture at varying temperature,” Journal of Building Materials, vol. 12, no. 5, pp. 625–630, 2009. View at: Google Scholar
 Z.J. Xue, J.N. Wang, and Y.Q. Tan, “Performance of reflection crack resistance of stressabsorbing waterproof interlayer,” Journal of South China University of Technology (Natural Science Edition), vol. 36, no. 10, pp. 81–85, 2008. View at: Google Scholar
 F. Xiao, S. Amirkhanian, H. Wang, and H. Wang, “Performance characteristics comparisons of various asphalt mixture technologies,” Journal of Testing and Evaluation, vol. 43, no. 4, pp. 841–852, 2014. View at: Publisher Site  Google Scholar
 F. Xiao, D. A. Herndon, S. Amirkhanian, and L. He, “Aggregate gradations on moisture and rutting resistances of open graded friction course mixtures,” Construction and Building Materials, vol. 85, pp. 127–135, 2015. View at: Publisher Site  Google Scholar
 J. F. Rushing and D. N. Little, “Static creep and repeated load as rutting performance tests for airport HMA mix design,” Journal of Materials in Civil Engineering, vol. 26, no. 9, Article ID 04014055, 2014. View at: Publisher Site  Google Scholar
 A. Ali, A. Abbas, M. Nazzal, A. Alhasan, A. Roy, and D. Powers, “Effect of temperature reduction, foaming water content, and aggregate moisture content on performance of foamed warm mix asphalt,” Construction and Building Materials, vol. 48, pp. 1058–1066, 2013. View at: Publisher Site  Google Scholar
 Z. Xie and J. Shen, “Performance properties of rubberized stone matrix asphalt mixtures produced through different processes,” Construction and Building Materials, vol. 104, pp. 230–234, 2016. View at: Publisher Site  Google Scholar
 H. Malladi, D. Ayyala, A. A. Tayebali, and N. P. Khosla, “Laboratory evaluation of warmmix asphalt mixtures for moisture and rutting susceptibility,” Journal of Materials in Civil Engineering, vol. 27, no. 5, Article ID 04014162, 2015. View at: Publisher Site  Google Scholar
 J. Zhang, J. Pei, and B. Wang, “Analysis of asphalt pavement rutting in continuously changing temperature field and early warning for high temperature,” Journal of Tongji University, vol. 39, no. 2, pp. 242–258, 2011. View at: Publisher Site  Google Scholar
 X. Huang, Y. Yang, H. Li et al., “Asphalt pavement shortterm rutting analysis and prediction considering temperature and traffic loading conditions,” Journal of South China University of Technology (English Edition), vol. 3, no. 3, pp. 1–24, 2009. View at: Google Scholar
 N.X. Zheng, S.S. Niu, and X.Q. Xu, “Temperature, axle load and axle load frequency model of rutting prediction of heavyduty asphalt pavement,” China Journal of Highway and Transport, vol. 22, no. 3, pp. 7–13, 2009. View at: Google Scholar
 X.Y. Gu, Q.Q. Yuan, and F.J. Ni, “Analysis of factors on asphalt pavement rut development based on measured load and temperature gradient,” China Journal of Highway and Transport, vol. 25, no. 6, pp. 30–36, 2012. View at: Google Scholar
 L. Zhou, N. Fujian, and Z. Yanjing, “Impact of Environment Temperature and Vehicle Loading on Rutting Development in Asphalt Concrete Pavement,” Journal of Highway and Transportation Research and Development, vol. 28, no. 3, pp. 42–47, 2011. View at: Google Scholar
 M. W. Witczak, K. Kaloush, T. Pellinen, and et al., “Simple performance test for Superpave mix design,” National Cooperative Highway Research Program (NCHRP) Report 465, Transportation Research Board, National Research Council, Washington, D.C., USA, 2002. View at: Google Scholar
 L. Peilong, S. Yanjun, and Z. Zhengqi, “Analysis of Rutting Deformation Characteristics on Asphalt Pavement and It’s Influencing Factors,” Subgrade Engineering, vol. 3, pp. 37–40, 2011. View at: Google Scholar
 D. Julong, “Grey Control System,” Journal of Huazhong University of Science and Technology, vol. 10, no. 3, pp. 9–18, 1982. View at: Google Scholar
Copyright
Copyright © 2017 Hui Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.