Adaptive neuro-fuzzy inference approach for prediction the stiffness ...
Advances in Engineering Software 45 (2012) 100–104
Contents lists available at SciVerse ScienceDirect
Advances in Engineering Software journal homepage: www.elsevier.com/locate/advengsoft
Adaptive neuro-fuzzy inference approach for prediction the stiffness modulus on asphalt concrete _ Ercan Özgan a,⇑, Ibrahim Korkmaz b, Mehmet Emirog˘lu a a b
Düzce University, Technical Education Faculty, Structural Department, Konuralp Campuse, Düzce, Turkey Düzce University, Düzce Vocational Higher School, Machine Department, Düzce, Turkey
a r t i c l e
i n f o
Article history: Received 21 May 2010 Received in revised form 27 June 2011 Accepted 31 August 2011 Available online 14 October 2011 Keywords: Asphalt concrete Stiffness modulus Prediction model Sugeno fuzzy inference Temperature effect Exposure times
a b s t r a c t In this study, stiffness modulus parameters of asphalt concrete were determined experimentally for different temperature and exposure times. The stiffness modules were calculated according to Nijboer stiffness module. Basic physical properties and the quantity of bitumen of asphalt core samples were designated for determining the stiffness modules. The samples were exposed to 17 °C (reference temperature), 30, 40 and 50 °C temperatures for 1.5, 3, 4.5 and 6 h respectively and then Marhall Stability tests were done for each samples. By using the test results a prediction model with Sugeno type based on the adaptive neuron-fuzzy inference system (ANFIS) was alternatively developed to predict the stiffness modules of asphalt core samples. As a result, it was seen that the developed prediction model could be used as a prediction model for unperformed situations which are not suitable for experiments. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Hot Mix Asphalt (HMA) is a combination of hot aggregate mix and asphalt cement and getting more and more versatile usage area in the world. HMA is used in the central and heavy traffic roads in order to sustain the traffic loads and protect from the negative effects of the outside conditions [9]. The asphalt concrete is combination of the three colloidal phases which are solid (aggregate and filler), fluid (asphalt) and gas (voids). The solid phase is provided the elasticity and ensured the shear stresses. The fluid phase makes the system visco-elastic and ensures the cohesion. The gas phase is affected the system indirectly and impressed some of the physical and mechanical properties of the mixture. Based on the temperature, the bitumen is exist the different rheological state such as brittle, elastic, elastoplastic, visco-elastic and viscous. If the bitumen is heated the consistency changes and this is one of the properties provide the use of the bitumen as binder material. Owing to the bitumen is thermoplastic material at the high temperatures it exhibits low strength. Especially in the summer time, the asphalt absorbs the heat and its deformation resistance is seriously decreased. On the contrary, at the lower temperatures the asphalt shoves the high strength. However, the hardening of the asphalt at the low temperature ⇑ Corresponding author. Tel.: +90 380 542 11 33; fax: +90 380 542 11 34. E-mail addresses: [email protected] (E. Özgan), ibrahimkorkmaz@ _ Korkmaz), [email protected] (M. Emirog˘lu). duzce.edu.tr (I. 0965-9978/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2011.09.015
caused the cracking and decreased the stability of the bitumen [18]. It is well known that mixing and compacting temperatures play a critical role in the physical and mechanical properties of compacted mixtures [8]. Hurley et al. [6] were used different compacting temperatures 149, 129, 110, and 88 °C and selected 19 °C mixing temperatures in their study. They indicated that resilient modulus decreased as compacting temperature decreased and air void would increase. Kok and Yilmaz [10] were prepared Marshall Specimens at 5.2% bitumen content. The halves of the total specimens were immersed in water at 60 °C for 30 min. and another half of the specimens were 60 °C for 24 h. and then loaded. It is indicated that Marshall Stability of the specimens were decreased as time exposure were increased. Edwards et al. [5] were studied the rheological effects of commercial waxes and polyphosphoric acid in bitumen at high and medium temperature. They indicated that adding polyethylene wax or polyphosphoric acid especially to a non-waxy bitumen, showed considerable positive effects on the rheological behavior at medium and higher temperatures. Parker [15] were studied the compaction of bituminous mixtures at various temperatures. It was found that the study of compaction temperatures could be conducted at a higher degree of correlation when compacted in a laboratory by the Marshall method than by cores from actual pavement construction. Stiffness modulus is pointed the relationship between stress and strain under the loading and it is signify the load distribution capacity of the mixture. Due to the stress–strain relationship of the
E. Özgan et al. / Advances in Engineering Software 45 (2012) 100–104
asphalt could not be fully reflected from the rheological models, visco-elastic behavior of the asphalt tried to define the stiffness modulus [18]. Stiffness modulus of the mixtures is changed based on the temperature, and the mix materials affected the second manner on the stiffness modulus [2,4,11]. Stability of asphalt concrete determines the performance of the highway pavement. Low stability in asphalt concrete may lead to various types of distress in asphalt pavements. The stability of asphalt concrete pavements depends on the stiffness of the mix, bitumen content, softening point of bitumen, viscosity of bitumen, grading of aggregate, construction practice, traffic and climate [13]. Sayin and Tanyildizi [16] were investigated the stiffness of the bitumen mixtures by using fuzzy logic according to Shell method. Because of the quality of bitumen must be chosen to adapt maximum and minimum temperatures they were used different temperature. They indicated that the experimental and the prediction results are matching each other. Özgan [14] were investigated the fuzzy logic and statistical-based modeling of the Marshall Stability of asphalt concrete under varying temperatures and exposure times. It was pointed out that the relationships between experimental results, fuzzy logic model and statistical results exhibited good correlation. The top asphalt layer is cold in the morning, hot during midday, and cool down in the evening. The bottom of asphalt layer may have an approximately constant temperature during the day or during different seasons (depending on the thickness) but varies during the year. Since HMA is thermally sensitive, the performance and distress of HMA are a function of temperature. Thermal cracks occur when the thermal stresses exceed the tensile strength of the material. A temperature drop of 22 °C to 18 °C can induce a thermal stress of 22 MPa on the asphalt. Chang and Meegoda [3] were investigated the mechanical behavior and internal structure of asphalt concrete due to change in different temperatures. They were used a micro-mechanical model to simulate the stress–strain behavior and variation of internal structure of asphalt concrete. The simulation they established showed the ability to predict the temperature susceptibility of the asphalt concrete. Stiffness modulus of asphalt concrete mixture is one of parameters for flexible pavement design that it is very susceptible from temperature and time loading. In this study, for determining the stiffness modulus of the asphalt concrete core samples obtained from the D100-11 Highway in Turkey have been used. On the 37 core samples, stiffness moduli have been determined by using Nijboer stiffness modulus method for different temperatures and exposure times. The samples were exposed to 17 °C (reference temperature), 30, 40 and 50 °C temperatures for 1.5, 3, 4.5 and 6 h respectively and then Marshall Stability tests were done and stability and failure loads were determined for each sample. As and alternative method Sugeno type prediction model based on the adaptive neuron-fuzzy inference system was developed to predict the stiffness modules of asphalt core samples in unperformed situation. 2. Materials and methods 2.1. Materials In the presented study, total 37 asphalt core samples with 10.16 cm diameter and 6.35 cm length were used and five samples from them were randomly selected as reference samples and waited in laboratory at 17 °C. Gravimetry of the samples were measured with 0.01 g sensitivity. The samples were turned to the saturated surface during 24 h in water tank at 16.2 °C. Volume of the core samples was calculated according to the equation given below:
V¼
ma ½ðmst þ mw Þ mst
qw
101
ð1Þ
V, is the volume of sample (cm3); ma, the mass of the samples in air (kg); mst , in appearance mass of the basket in water (kg); mw , in appearance mass of the samples in water (kg) and qw, is the density of water at 20 °C temperature (998 kg/m3). According to the volume of samples, volume of voids, specific gravity for saturated surface and dry specific gravity were calculated for each sample. After determined the basic physical properties of the core samples Marshall Stability tests were conducted and the values of flow were measured for each core samples at the end of the different temperature and exposure times. The extraction machine with 3600 cycle/min was used to determine the quantity of bitumen in the core samples. Three-chloral ethylene was used as a solvent material to decompose the bitumen from the aggregate. The basic physical properties, Marshall Stability values, the quantity of the bitumen and the flow values of the samples were summarized in (Table 1). 2.2. Stiffness modules The core samples were respectively waited at 17 °C (reference value), 30, 40 and 50 °C temperature and immediately exposed to the Marshall Stability test for each temperatures. The stiffness modules of the core samples were calculated by Eq. (2) and the test set-up of the Marshall Stability test on core samples was shown in Fig. 1.
SN ¼
r AP P d ¼ ) e Fd A F
ð2Þ
where SN , is the stiffness module kg/cm2; P, the Marshall Stability (max. load) kg; F, the flow (vertical moving for max. load in ‘‘y’’ axis) mm; A, the cross section area that straights to the load (d L) cm2; d, the diameter of the sample (10.16 cm) cm and (L, is the length of the sample is 6.35 cm). 3. ANFIS (adaptive neuro-fuzzy inference system) Fuzzy systems use fuzzy sets with the aim of converting input variables to output variables [17]. These systems are beneficial especially in adding human experiences and verbal data to the model. For this purpose variables of the model are expressed with fuzzy sub-sets. For the inference under consideration fuzzy set operations, which are obtained by generalizing classical set operations, are used. Fuzzy logic is one of the methods which are used in handling the uncertainties in the model or the data. Fuzzy inference systems are based on fuzzy rules which are called fuzzy ifthen rules. In some resources instead of fuzzy inference systems terms such as fuzzy model, fuzzy associative memory and fuzzy logic controller are also used [7]. Fuzzy if-then rules which are the fundamentals of fuzzy inference systems consist of, as it can be understood, anterior and posterior portions. Input variables which cause the result and the logical relationships between them are present in the anterior portion whereas result variables that appear according to these input variables are located in posterior portion. Generally this fuzzy rule is as given below:
Rule : if Að\condition"Þ then Bð\result"Þ Here A represents the conditions that are defined by input variables in anterior portion while B represents the output value in posterior portion. Numerous and various models are proposed for fuzzy inference systems in application [6]. Despite the fact that these resemble each other from general process sequence and methodology point of view they differ in terms of structures of membership functions
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Table 1 Basic physical properties, Marshall Stability, the quantity of the bitumen and the flow values of the samples. Parameters 3
Air dry specific gravity (g/cm ) Temperature (°C) Time (h) Quantity of the bitumen (g) Marshall Stability (kg) Flow (mm)
N
Range
Min.
Max.
Mean
Std. error
Std. dev.
Variance
26 26 26 26 26 26
0.25 33 6 63.60 3883 4.93
2.38 17 0 80.70 536 4.06
2.63 50 6 144.30 4419 8.99
2.5162 38.2308 3.4615 1.03452 1.55373 5.8446
0.01220 1.99099 0.37919 3.60584 2.062542 0.22305
0.06223 10.15207 1.93351 18.38624 1051.69452 1.13734
0004 103.065 3.738 338.054 1.1066 1.294
Fig. 1. Test set-up of the Marshall Stability test on core samples.
in posterior portions. Fuzzy inference systems are categorized in three different groups according to these differences in posterior portions. These are Mamdani, Tsukamoto and Sugeno type inference systems. Of these Sugeno type inference system is more advantageous than the rest due to the ease of parameter optimization. In Sugeno type FIS output variable in posterior portion is a linear function of the input variable or it has a membership function in the form of a constant function. The Sugeno type inference systems, parameters of which are optimized, are called adaptive network FIS (ANFIS). Two fuzzy ruled Sugeno type FIS are shown in Fig. 2 [7]. In optimization of ANFIS parameters various methods such as backward spreading, least squares estimation, Kalman filter, or hybrid learning algorithms which consist of combination of multiple mathematical optimization methods can be used [1]. In this study ‘‘hybrid method’’ is used. Rules in Sugeno type fuzzy inference systems are expressed as:
If eAi and yeBj then zk ¼ fkðx; yÞ Here A and B are the labels of sets which divide X and Y variable spaces in the anterior portion into fuzzy sub spaces, respectively, whereas zk is (with k = ixj) the output value corresponding to that rule and it is a function of input variable. Result output value for any x, y input pair is the weighted average of zk’s which are the output values of all rules (Fig. 2).
4. Prediction of the stiffness module with ANFIS By using Sugeno type fuzzy inferences method a prediction model was developed to predict the stiffness of the asphalt core samples. In the training and testing processing of the model totally 37 data sets were used. Input parameters of the model are temperature, exposure time, the quantity of the bitumen and air dry specific gravity. As 29 data sets were used for training the model, 8 data sets were used for testing the confidence of the model. In
Fig. 2. Sugeno type fuzzy model.
E. Özgan et al. / Advances in Engineering Software 45 (2012) 100–104
103
(a) General architecture of the Sugeno type fuzz inference system
(b) Membership function for air dry specific gravity (g/cm3)
(d) Membership function for time (hour)
(c) Membership function for temperature (oC)
(e) Membership function for the quantity of bitumen (g)
Fig. 3. Determined membership functions, general architecture of the model and membership functions of the inputs. (a) General architecture of the Sugeno type fuzz inference system, (b) membership function for air dry specific gravity (g/cm3), (c) membership function for temperature (°C), (d) membership function for time (h) and (e) membership function for the quantity of bitumen (g).
Fig. 4. A part of the rules in the model.
the training of the model, different optimization methods were trained in different iteration to establish the most suitable model which was the best represented of the experimental test result and given the least mean square error. There are 0.5, 1.25, 0.5, 0.15 values for ranges of influence, squash factor, accept ratio, and reject ratio. Also the optimum method is hybrid. The number of the membership functions for each one input variables are 5 with ‘‘trimf’’ type in the training process. Number of iteration is 160, number of nodes are 1297, number of linear parameters are
3125, number of nonlinear parameters are 60, total number of parameters are 3185, number of training data pairs are 26, and number of fuzzy rules are 625 respectively. In the rule base, fuzzy variables were connected with ‘‘prod’’ operators and the implication of the each rule was calculated using ‘‘wtaver’’ (weighted average) defuzzification method. The correlation coefficient was found as 0.97 for training set. When the number of the membership function less than 5, the changing ranges of the data were not represented by the model [12]. Determined membership functions,
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Table 2 Calculated stiffness module and predicted stiffness module. Calculated stiffness module
Predicted stiffness module
474.12 493.86 422.06 213.72 267.45 322.87 192.83 255.52
656 701 444 202 237 347 211 216
Then Marshall Stability test was conducted on these samples and the flow values were recorded for each one sample. The bitumen quantity of the core samples were determined by conducting extraction test with 3600 cycle/min rotary extraction machine. It was seen from the experimental test results that according to the environment temperature the viscosity of the bitumen are decreasing and the bitumen begin to flow so that increasing environment temperature decrease the stiffness of the asphalt core samples. However, the exposure time has effected the stiffness of the samples as well as temperature. In the developed prediction model used Sugeno type adaptive neuro-fuzzy inference system inputs parameters are specific gravity (g/cm3), temperature (°C), exposure time (h) and the quantity of the bitumen (g) and the out put parameter is stiffness module (kg/cm2) of the samples. In the training process totally 625 rules were occurred that are include all of the possible combination between inputs. The correlation coefficient was found highly important with 0.94. As a result it could be said that the prediction model can be used for unknown status. References
Fig. 5. Stiffness module and the correlation coefficient between calculated and predicted results.
general architecture of the model which was made after the training process and the membership functions of the inputs were showed together in Fig. 3a–e. On the training, the number of the rules is 625. The rules are including all of the possible combinations between inputs. The model screen for a part of the rules was showed in Fig. 4. In the training and testing processing of the model totally 37 data sets were used. As 29 data sets were used for training of the model, 8 data sets were used for testing the confidence of the model. The values of the stiffness model for experimental test and prediction models were given in Table 2. The results of the model and experimental test results were compared with together and it was seen that there is a good correlation between the results (Fig. 5). 5. Result and recommendations To determine the stiffness module of asphalt concrete in different temperature and exposure time the number of 37 core samples were taken from in field and the samples waited at 17 °C (reference temperature), 30, 40, and 50 °C for 1.5, 3, 4.5, and 6 h respectively.
[1] Akyılmaz O, Ayan T, Özlüdemir MT. Geoid surface approximation by using Adaptive Network based Fuzzy Inference Systems. Allg Vermessungs-Nachr 2003;8(9):22–7. [2] Ahmetzade P, Sengoz B. Evaluation of steel slag coarse aggregate in hot mix asphalt concrete. J Hazard Mater 2008;165:300–5. [3] Chang GK, Meegoda JN. Micromechanical model for temperature effects of hotmix asphalt concrete. Transportation Research Record No. 1687; 1999. p. 95– 103. [4] Chen JS, Kuo PH, Lin PS, Huang CC, Lin KY. Experimental and theoretical characterization of the engineering behavior of bitumen mixed with mineral filler. Mater Struct 2008;41:1015–24. [5] Edwards Y, Tasdemir Y, Isacsson U. Rheological effects of commercial waxes and polyphosphoric acid in bitumen 160/220 – high and medium temperature performance. Constr Build Mater 2007;21:1899–908. [6] Hurley GC, Prowell BD, Reinke G, Joskowicz P, Davis R, Scherocman J, et al. Evaluation of potential process for use in warm mix asphalt. J Assoc Asphalt Paving Technol 2006;75:41–90. [7] Jang JSR, Sun CT, Mizutani E. Neuro-fuzzy and soft computing. Prentice Hall; 1997. [8] Kennedy TW, Roberts FL, Mc Gennis RB. Effects of compaction temperature and effort on the engineering properties of asphalt mixtures. In: Wagner FT, editor. ASTM STP 829. American Society for Testing Materials; 1984. p. 48–66. [9] Kok BV, Kuloglu N. The effects of different binders on mechanical properties of hot mix asphalt. Int J Sci Technol 2007;2(1):41–8. [10] Kok BV, Yilmaz M. The effects of using lime and styrene–butadiene–styrene on moisture sensitivity resistance of hot mix asphalt. Constr Build Mater 2009;23:1999–2006. [11] Lefeuvre Y, de La Roche C, Piau JM. Asphalt material fatigue test under cyclic loading: the lengthening of samples as a way to characterize the material damage experiments and modelling. Mater Struct 2005;38:115–9. [12] Matlab documentation set. The MathWorks Inc.; 2004. [13] Özgan E. Determining the stability of asphalt concrete at varying temperatures and exposure times using destructive and non-destructive method. J. Appl. Sci. 2007;7(24):3870–9. [14] Özgan E. Fuzzy logic and statistical-based modelling of the Marshall Stability of asphalt concrete under varying temperatures and exposure times. Adv Eng Softw 2009;40:527–34. [15] Parker CF. Effect of mix temperature. Highway research board special report, vol. 54; 1960. p. 28–33. [16] Sayin E, Tanyildizi H. Bitümlü sıcak karısßımların rijitlig˘inin bulanık mantık ile bulunması. J Fac Eng Arch Gazi Univ 2006;21(4):645–9 [in Turkish]. [17] Zadeh LA. Fuzzy sets. Inf Control 1965;8:338–52. [18] Zaimog˘lu F. Beton Asfalt Kaplamalarda Rjitlik Modülünün Shell Metodu ve _ Indirek Çekme Metodu ile Karsßılasßtırılması, Fırat Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi; 2005 [in Turkish].
Contents lists available at SciVerse ScienceDirect
Advances in Engineering Software journal homepage: www.elsevier.com/locate/advengsoft
Adaptive neuro-fuzzy inference approach for prediction the stiffness modulus on asphalt concrete _ Ercan Özgan a,⇑, Ibrahim Korkmaz b, Mehmet Emirog˘lu a a b
Düzce University, Technical Education Faculty, Structural Department, Konuralp Campuse, Düzce, Turkey Düzce University, Düzce Vocational Higher School, Machine Department, Düzce, Turkey
a r t i c l e
i n f o
Article history: Received 21 May 2010 Received in revised form 27 June 2011 Accepted 31 August 2011 Available online 14 October 2011 Keywords: Asphalt concrete Stiffness modulus Prediction model Sugeno fuzzy inference Temperature effect Exposure times
a b s t r a c t In this study, stiffness modulus parameters of asphalt concrete were determined experimentally for different temperature and exposure times. The stiffness modules were calculated according to Nijboer stiffness module. Basic physical properties and the quantity of bitumen of asphalt core samples were designated for determining the stiffness modules. The samples were exposed to 17 °C (reference temperature), 30, 40 and 50 °C temperatures for 1.5, 3, 4.5 and 6 h respectively and then Marhall Stability tests were done for each samples. By using the test results a prediction model with Sugeno type based on the adaptive neuron-fuzzy inference system (ANFIS) was alternatively developed to predict the stiffness modules of asphalt core samples. As a result, it was seen that the developed prediction model could be used as a prediction model for unperformed situations which are not suitable for experiments. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Hot Mix Asphalt (HMA) is a combination of hot aggregate mix and asphalt cement and getting more and more versatile usage area in the world. HMA is used in the central and heavy traffic roads in order to sustain the traffic loads and protect from the negative effects of the outside conditions [9]. The asphalt concrete is combination of the three colloidal phases which are solid (aggregate and filler), fluid (asphalt) and gas (voids). The solid phase is provided the elasticity and ensured the shear stresses. The fluid phase makes the system visco-elastic and ensures the cohesion. The gas phase is affected the system indirectly and impressed some of the physical and mechanical properties of the mixture. Based on the temperature, the bitumen is exist the different rheological state such as brittle, elastic, elastoplastic, visco-elastic and viscous. If the bitumen is heated the consistency changes and this is one of the properties provide the use of the bitumen as binder material. Owing to the bitumen is thermoplastic material at the high temperatures it exhibits low strength. Especially in the summer time, the asphalt absorbs the heat and its deformation resistance is seriously decreased. On the contrary, at the lower temperatures the asphalt shoves the high strength. However, the hardening of the asphalt at the low temperature ⇑ Corresponding author. Tel.: +90 380 542 11 33; fax: +90 380 542 11 34. E-mail addresses: [email protected] (E. Özgan), ibrahimkorkmaz@ _ Korkmaz), [email protected] (M. Emirog˘lu). duzce.edu.tr (I. 0965-9978/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2011.09.015
caused the cracking and decreased the stability of the bitumen [18]. It is well known that mixing and compacting temperatures play a critical role in the physical and mechanical properties of compacted mixtures [8]. Hurley et al. [6] were used different compacting temperatures 149, 129, 110, and 88 °C and selected 19 °C mixing temperatures in their study. They indicated that resilient modulus decreased as compacting temperature decreased and air void would increase. Kok and Yilmaz [10] were prepared Marshall Specimens at 5.2% bitumen content. The halves of the total specimens were immersed in water at 60 °C for 30 min. and another half of the specimens were 60 °C for 24 h. and then loaded. It is indicated that Marshall Stability of the specimens were decreased as time exposure were increased. Edwards et al. [5] were studied the rheological effects of commercial waxes and polyphosphoric acid in bitumen at high and medium temperature. They indicated that adding polyethylene wax or polyphosphoric acid especially to a non-waxy bitumen, showed considerable positive effects on the rheological behavior at medium and higher temperatures. Parker [15] were studied the compaction of bituminous mixtures at various temperatures. It was found that the study of compaction temperatures could be conducted at a higher degree of correlation when compacted in a laboratory by the Marshall method than by cores from actual pavement construction. Stiffness modulus is pointed the relationship between stress and strain under the loading and it is signify the load distribution capacity of the mixture. Due to the stress–strain relationship of the
E. Özgan et al. / Advances in Engineering Software 45 (2012) 100–104
asphalt could not be fully reflected from the rheological models, visco-elastic behavior of the asphalt tried to define the stiffness modulus [18]. Stiffness modulus of the mixtures is changed based on the temperature, and the mix materials affected the second manner on the stiffness modulus [2,4,11]. Stability of asphalt concrete determines the performance of the highway pavement. Low stability in asphalt concrete may lead to various types of distress in asphalt pavements. The stability of asphalt concrete pavements depends on the stiffness of the mix, bitumen content, softening point of bitumen, viscosity of bitumen, grading of aggregate, construction practice, traffic and climate [13]. Sayin and Tanyildizi [16] were investigated the stiffness of the bitumen mixtures by using fuzzy logic according to Shell method. Because of the quality of bitumen must be chosen to adapt maximum and minimum temperatures they were used different temperature. They indicated that the experimental and the prediction results are matching each other. Özgan [14] were investigated the fuzzy logic and statistical-based modeling of the Marshall Stability of asphalt concrete under varying temperatures and exposure times. It was pointed out that the relationships between experimental results, fuzzy logic model and statistical results exhibited good correlation. The top asphalt layer is cold in the morning, hot during midday, and cool down in the evening. The bottom of asphalt layer may have an approximately constant temperature during the day or during different seasons (depending on the thickness) but varies during the year. Since HMA is thermally sensitive, the performance and distress of HMA are a function of temperature. Thermal cracks occur when the thermal stresses exceed the tensile strength of the material. A temperature drop of 22 °C to 18 °C can induce a thermal stress of 22 MPa on the asphalt. Chang and Meegoda [3] were investigated the mechanical behavior and internal structure of asphalt concrete due to change in different temperatures. They were used a micro-mechanical model to simulate the stress–strain behavior and variation of internal structure of asphalt concrete. The simulation they established showed the ability to predict the temperature susceptibility of the asphalt concrete. Stiffness modulus of asphalt concrete mixture is one of parameters for flexible pavement design that it is very susceptible from temperature and time loading. In this study, for determining the stiffness modulus of the asphalt concrete core samples obtained from the D100-11 Highway in Turkey have been used. On the 37 core samples, stiffness moduli have been determined by using Nijboer stiffness modulus method for different temperatures and exposure times. The samples were exposed to 17 °C (reference temperature), 30, 40 and 50 °C temperatures for 1.5, 3, 4.5 and 6 h respectively and then Marshall Stability tests were done and stability and failure loads were determined for each sample. As and alternative method Sugeno type prediction model based on the adaptive neuron-fuzzy inference system was developed to predict the stiffness modules of asphalt core samples in unperformed situation. 2. Materials and methods 2.1. Materials In the presented study, total 37 asphalt core samples with 10.16 cm diameter and 6.35 cm length were used and five samples from them were randomly selected as reference samples and waited in laboratory at 17 °C. Gravimetry of the samples were measured with 0.01 g sensitivity. The samples were turned to the saturated surface during 24 h in water tank at 16.2 °C. Volume of the core samples was calculated according to the equation given below:
V¼
ma ½ðmst þ mw Þ mst
qw
101
ð1Þ
V, is the volume of sample (cm3); ma, the mass of the samples in air (kg); mst , in appearance mass of the basket in water (kg); mw , in appearance mass of the samples in water (kg) and qw, is the density of water at 20 °C temperature (998 kg/m3). According to the volume of samples, volume of voids, specific gravity for saturated surface and dry specific gravity were calculated for each sample. After determined the basic physical properties of the core samples Marshall Stability tests were conducted and the values of flow were measured for each core samples at the end of the different temperature and exposure times. The extraction machine with 3600 cycle/min was used to determine the quantity of bitumen in the core samples. Three-chloral ethylene was used as a solvent material to decompose the bitumen from the aggregate. The basic physical properties, Marshall Stability values, the quantity of the bitumen and the flow values of the samples were summarized in (Table 1). 2.2. Stiffness modules The core samples were respectively waited at 17 °C (reference value), 30, 40 and 50 °C temperature and immediately exposed to the Marshall Stability test for each temperatures. The stiffness modules of the core samples were calculated by Eq. (2) and the test set-up of the Marshall Stability test on core samples was shown in Fig. 1.
SN ¼
r AP P d ¼ ) e Fd A F
ð2Þ
where SN , is the stiffness module kg/cm2; P, the Marshall Stability (max. load) kg; F, the flow (vertical moving for max. load in ‘‘y’’ axis) mm; A, the cross section area that straights to the load (d L) cm2; d, the diameter of the sample (10.16 cm) cm and (L, is the length of the sample is 6.35 cm). 3. ANFIS (adaptive neuro-fuzzy inference system) Fuzzy systems use fuzzy sets with the aim of converting input variables to output variables [17]. These systems are beneficial especially in adding human experiences and verbal data to the model. For this purpose variables of the model are expressed with fuzzy sub-sets. For the inference under consideration fuzzy set operations, which are obtained by generalizing classical set operations, are used. Fuzzy logic is one of the methods which are used in handling the uncertainties in the model or the data. Fuzzy inference systems are based on fuzzy rules which are called fuzzy ifthen rules. In some resources instead of fuzzy inference systems terms such as fuzzy model, fuzzy associative memory and fuzzy logic controller are also used [7]. Fuzzy if-then rules which are the fundamentals of fuzzy inference systems consist of, as it can be understood, anterior and posterior portions. Input variables which cause the result and the logical relationships between them are present in the anterior portion whereas result variables that appear according to these input variables are located in posterior portion. Generally this fuzzy rule is as given below:
Rule : if Að\condition"Þ then Bð\result"Þ Here A represents the conditions that are defined by input variables in anterior portion while B represents the output value in posterior portion. Numerous and various models are proposed for fuzzy inference systems in application [6]. Despite the fact that these resemble each other from general process sequence and methodology point of view they differ in terms of structures of membership functions
102
E. Özgan et al. / Advances in Engineering Software 45 (2012) 100–104
Table 1 Basic physical properties, Marshall Stability, the quantity of the bitumen and the flow values of the samples. Parameters 3
Air dry specific gravity (g/cm ) Temperature (°C) Time (h) Quantity of the bitumen (g) Marshall Stability (kg) Flow (mm)
N
Range
Min.
Max.
Mean
Std. error
Std. dev.
Variance
26 26 26 26 26 26
0.25 33 6 63.60 3883 4.93
2.38 17 0 80.70 536 4.06
2.63 50 6 144.30 4419 8.99
2.5162 38.2308 3.4615 1.03452 1.55373 5.8446
0.01220 1.99099 0.37919 3.60584 2.062542 0.22305
0.06223 10.15207 1.93351 18.38624 1051.69452 1.13734
0004 103.065 3.738 338.054 1.1066 1.294
Fig. 1. Test set-up of the Marshall Stability test on core samples.
in posterior portions. Fuzzy inference systems are categorized in three different groups according to these differences in posterior portions. These are Mamdani, Tsukamoto and Sugeno type inference systems. Of these Sugeno type inference system is more advantageous than the rest due to the ease of parameter optimization. In Sugeno type FIS output variable in posterior portion is a linear function of the input variable or it has a membership function in the form of a constant function. The Sugeno type inference systems, parameters of which are optimized, are called adaptive network FIS (ANFIS). Two fuzzy ruled Sugeno type FIS are shown in Fig. 2 [7]. In optimization of ANFIS parameters various methods such as backward spreading, least squares estimation, Kalman filter, or hybrid learning algorithms which consist of combination of multiple mathematical optimization methods can be used [1]. In this study ‘‘hybrid method’’ is used. Rules in Sugeno type fuzzy inference systems are expressed as:
If eAi and yeBj then zk ¼ fkðx; yÞ Here A and B are the labels of sets which divide X and Y variable spaces in the anterior portion into fuzzy sub spaces, respectively, whereas zk is (with k = ixj) the output value corresponding to that rule and it is a function of input variable. Result output value for any x, y input pair is the weighted average of zk’s which are the output values of all rules (Fig. 2).
4. Prediction of the stiffness module with ANFIS By using Sugeno type fuzzy inferences method a prediction model was developed to predict the stiffness of the asphalt core samples. In the training and testing processing of the model totally 37 data sets were used. Input parameters of the model are temperature, exposure time, the quantity of the bitumen and air dry specific gravity. As 29 data sets were used for training the model, 8 data sets were used for testing the confidence of the model. In
Fig. 2. Sugeno type fuzzy model.
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(a) General architecture of the Sugeno type fuzz inference system
(b) Membership function for air dry specific gravity (g/cm3)
(d) Membership function for time (hour)
(c) Membership function for temperature (oC)
(e) Membership function for the quantity of bitumen (g)
Fig. 3. Determined membership functions, general architecture of the model and membership functions of the inputs. (a) General architecture of the Sugeno type fuzz inference system, (b) membership function for air dry specific gravity (g/cm3), (c) membership function for temperature (°C), (d) membership function for time (h) and (e) membership function for the quantity of bitumen (g).
Fig. 4. A part of the rules in the model.
the training of the model, different optimization methods were trained in different iteration to establish the most suitable model which was the best represented of the experimental test result and given the least mean square error. There are 0.5, 1.25, 0.5, 0.15 values for ranges of influence, squash factor, accept ratio, and reject ratio. Also the optimum method is hybrid. The number of the membership functions for each one input variables are 5 with ‘‘trimf’’ type in the training process. Number of iteration is 160, number of nodes are 1297, number of linear parameters are
3125, number of nonlinear parameters are 60, total number of parameters are 3185, number of training data pairs are 26, and number of fuzzy rules are 625 respectively. In the rule base, fuzzy variables were connected with ‘‘prod’’ operators and the implication of the each rule was calculated using ‘‘wtaver’’ (weighted average) defuzzification method. The correlation coefficient was found as 0.97 for training set. When the number of the membership function less than 5, the changing ranges of the data were not represented by the model [12]. Determined membership functions,
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Table 2 Calculated stiffness module and predicted stiffness module. Calculated stiffness module
Predicted stiffness module
474.12 493.86 422.06 213.72 267.45 322.87 192.83 255.52
656 701 444 202 237 347 211 216
Then Marshall Stability test was conducted on these samples and the flow values were recorded for each one sample. The bitumen quantity of the core samples were determined by conducting extraction test with 3600 cycle/min rotary extraction machine. It was seen from the experimental test results that according to the environment temperature the viscosity of the bitumen are decreasing and the bitumen begin to flow so that increasing environment temperature decrease the stiffness of the asphalt core samples. However, the exposure time has effected the stiffness of the samples as well as temperature. In the developed prediction model used Sugeno type adaptive neuro-fuzzy inference system inputs parameters are specific gravity (g/cm3), temperature (°C), exposure time (h) and the quantity of the bitumen (g) and the out put parameter is stiffness module (kg/cm2) of the samples. In the training process totally 625 rules were occurred that are include all of the possible combination between inputs. The correlation coefficient was found highly important with 0.94. As a result it could be said that the prediction model can be used for unknown status. References
Fig. 5. Stiffness module and the correlation coefficient between calculated and predicted results.
general architecture of the model which was made after the training process and the membership functions of the inputs were showed together in Fig. 3a–e. On the training, the number of the rules is 625. The rules are including all of the possible combinations between inputs. The model screen for a part of the rules was showed in Fig. 4. In the training and testing processing of the model totally 37 data sets were used. As 29 data sets were used for training of the model, 8 data sets were used for testing the confidence of the model. The values of the stiffness model for experimental test and prediction models were given in Table 2. The results of the model and experimental test results were compared with together and it was seen that there is a good correlation between the results (Fig. 5). 5. Result and recommendations To determine the stiffness module of asphalt concrete in different temperature and exposure time the number of 37 core samples were taken from in field and the samples waited at 17 °C (reference temperature), 30, 40, and 50 °C for 1.5, 3, 4.5, and 6 h respectively.
[1] Akyılmaz O, Ayan T, Özlüdemir MT. Geoid surface approximation by using Adaptive Network based Fuzzy Inference Systems. Allg Vermessungs-Nachr 2003;8(9):22–7. [2] Ahmetzade P, Sengoz B. Evaluation of steel slag coarse aggregate in hot mix asphalt concrete. J Hazard Mater 2008;165:300–5. [3] Chang GK, Meegoda JN. Micromechanical model for temperature effects of hotmix asphalt concrete. Transportation Research Record No. 1687; 1999. p. 95– 103. [4] Chen JS, Kuo PH, Lin PS, Huang CC, Lin KY. Experimental and theoretical characterization of the engineering behavior of bitumen mixed with mineral filler. Mater Struct 2008;41:1015–24. [5] Edwards Y, Tasdemir Y, Isacsson U. Rheological effects of commercial waxes and polyphosphoric acid in bitumen 160/220 – high and medium temperature performance. Constr Build Mater 2007;21:1899–908. [6] Hurley GC, Prowell BD, Reinke G, Joskowicz P, Davis R, Scherocman J, et al. Evaluation of potential process for use in warm mix asphalt. J Assoc Asphalt Paving Technol 2006;75:41–90. [7] Jang JSR, Sun CT, Mizutani E. Neuro-fuzzy and soft computing. Prentice Hall; 1997. [8] Kennedy TW, Roberts FL, Mc Gennis RB. Effects of compaction temperature and effort on the engineering properties of asphalt mixtures. In: Wagner FT, editor. ASTM STP 829. American Society for Testing Materials; 1984. p. 48–66. [9] Kok BV, Kuloglu N. The effects of different binders on mechanical properties of hot mix asphalt. Int J Sci Technol 2007;2(1):41–8. [10] Kok BV, Yilmaz M. The effects of using lime and styrene–butadiene–styrene on moisture sensitivity resistance of hot mix asphalt. Constr Build Mater 2009;23:1999–2006. [11] Lefeuvre Y, de La Roche C, Piau JM. Asphalt material fatigue test under cyclic loading: the lengthening of samples as a way to characterize the material damage experiments and modelling. Mater Struct 2005;38:115–9. [12] Matlab documentation set. The MathWorks Inc.; 2004. [13] Özgan E. Determining the stability of asphalt concrete at varying temperatures and exposure times using destructive and non-destructive method. J. Appl. Sci. 2007;7(24):3870–9. [14] Özgan E. Fuzzy logic and statistical-based modelling of the Marshall Stability of asphalt concrete under varying temperatures and exposure times. Adv Eng Softw 2009;40:527–34. [15] Parker CF. Effect of mix temperature. Highway research board special report, vol. 54; 1960. p. 28–33. [16] Sayin E, Tanyildizi H. Bitümlü sıcak karısßımların rijitlig˘inin bulanık mantık ile bulunması. J Fac Eng Arch Gazi Univ 2006;21(4):645–9 [in Turkish]. [17] Zadeh LA. Fuzzy sets. Inf Control 1965;8:338–52. [18] Zaimog˘lu F. Beton Asfalt Kaplamalarda Rjitlik Modülünün Shell Metodu ve _ Indirek Çekme Metodu ile Karsßılasßtırılması, Fırat Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi; 2005 [in Turkish].
