[american society of civil engineers 2013 airfield & highway pavement conference - los angeles,...

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Modeling Pavement Temperature Prediction using Artificial Neural Networks

Mostafa A. Abo-Hashema1

1 Professor of Highway Engineering, Department of Civil Engineering, Fayoum University, P.O. Box 24 63511, Fayoum City, Egypt, PH (+20) 106 281 0128, FAX (+20) 84 633 4031, email: [email protected]

ABSTRACT

One of the key elements in the Mechanistic-Empirical (M-E) design system of flexible pavements is a pavement temperature prediction model. Many regression models have been developed to predict the temperature of Asphalt Concrete (AC) layer using air temperature with some other input parameters. Some of these models are old and cannot be applied to various site locations with accuracy. Others are quite accurate but they require many input data parameters that may not be available to the ordinary practitioner. Therefore, this paper discusses the feasibility of applying Artificial Neural Network (ANN) technology in predicting the AC layer temperature. The neural network has been trained and tested using NeuroSolutions 5.0 software through actual field data obtained from Long-Term Pavement Performance (LTPP), Seasonal Monitoring Program (SMP) - DataPave3.0 software. Two ANN models have been created: first is based on air temperature together with some other parameters and the second is based only on air temperature for simplicity. Results indicated that the developed ANN-based pavement temperature prediction models can be used in predicting AC layer temperature with high accuracy as compared to measured values. This outcome is considered crucial to the pavement design especially the second ANN model where some input parameters may not be available. KEY WORDS: pavement temperature, neural network, ann, prediction model, pavement design

490Airfield and Highway Pavement 2013: Sustainable and Efficient Pavements © ASCE 2013

Airfield and Highway Pavement 2013

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1. INTRODUCTION

Flexible pavement design system is highly affected by the structural capacity of pavement layers, which in turn depends on the modulus of resilience of these layers. While the modulus of the Asphalt Concrete (AC) layers is more sensitive to temperature, the modulus of unbound materials, such as base/subbase and subgrade, is sensitive to variation of moisture content. These two environmental factors, temperature and moisture content, must be incorporated in the design process of flexible pavements [Abo-Hashema et al. 2007, Abo-Hashema and Bayomy 2002]. For asphalt bound materials, temperature would be the factor effecting the variation of layer moduli, exhibiting modulus increase at lower temperatures and modulus decrease at higher temperatures. Determination of seasonal moduli values of AC materials requires selection of a representative seasonal pavement temperature and then evaluating the asphalt concrete modulus at that temperature [Abo-Hashema and Bayomy 2002, Bayomy and Abo-Hashema 2001]. Therefore, a pavement temperature prediction model is considered a key element in a Mechanistic-Empirical (M-E) design system for flexible pavements to predict the seasonal pavement temperature, used to alter the modulus of the AC layers at different seasons. Several regression models to predict asphalt pavement temperature have been developed. Some of these models are old and cannot be applied to various site locations with accuracy. Others are quite accurate but require many input data parameters that may not be available to the ordinary practitioner. “Over the past two decades, there has been an increased interest in a new class of computational intelligence systems known as Artificial Neural Networks (ANNs). This type of networks has been found to be powerful and versatile computational tool for organizing and correlating information in ways that have proved useful for solving certain types of problems too complex, too poorly understood, or too resource-intensive to tackle using more-traditional computational methods. ANNs have been successfully used for many tasks including pattern recognition, function approximation, optimization, forecasting, data retrieval, and automatic control [A2K05 1999].” This paper presents an ANN-based asphalt pavement temperature prediction model. The ANN model has been trained and validated using NeuroSolutions 5.0 software [Lefebvre et al. 2005] through data obtained from Long-Term Pavement Performance (LTPP), Seasonal Monitoring Program (SMP) - DataPave3.0 software [DataPave3.0 2001]. This is particularly promising for developing countries where some input parameters to predict the pavement temperature may not be available.



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2. PAVEMENT TEMPERATURE PREDICTION MODELS

This section briefly reviews the most popular asphalt pavement temperature prediction models. It shows also how much data required for each model to predict AC temperature.

2.1 BELLS Equations

A series of pavement temperature prediction models has been recently developed using data from the LTPP-SMP. Named BELLS after the first letters of the authors’ names, the primary model predicted the pavement temperature at various depths using the AC layer thickness, 5-day mean air temperatures, infrared surface temperature reading, and time of day. Because defective infrared surface temperature probes were used during data collection, the first BELLS equation is only valid for a temperature range of 15oC to 25oC [Stubstad et al. 1994, Stubstad et al. 1998, Lukanen et al. 2000]. A second model, BELLS2, was developed using corrected infrared surface temperature data. To decrease the amount of data required to use the model, the 5-day mean air temperature was replaced by the average of the previous day’s high and low air temperatures. As a consequence of the LTPP testing protocol under which the temperature data was obtained, the pavement surface was shaded for an average of 6 min prior to temperature sampling. So, the BELLS2 model is based on biased surface temperatures. A third model, BELLS3, was therefore developed for use during routine Falling Weight Deflectometer (FWD) testing when the pavement surface is typically shaded for less than a minute. The BELLS3 equation for use during routine testing is [Stubstad et al. 1994, Stubstad et al. 1998]:

( )[ ]

)5.13sin(**042.0

)5.15sin(*83.1

)1(*621.0*448.0*25.1log*892.095.0

18

18

−+

⎥⎦

⎤⎢⎣

⎡−+

−+−−++=

hrIR

hr

dayIRdIRTP

(1) where Tp = Pavement temperature at depth d, oC; IR = Infrared surface temperature, oC; Log = Base 10 logarithm; d = Depth at which temperature is to be predicted, mm (greater than zero); 1-day = Average air temperature the day before testing; hr18 = Time of day on a 24-hr clock system, but calculated using an 18-hr AC temperature rise-and-fall time cycle. When using the sin (hr18 – 15.5), the decimal form for the time is used. For example, if the time is 13:25, then in decimal form, 13.25-15.5 = -2.25; -2.25/18= -0.125; -0.125x2π = -0.785 radians; sin (-0.785) = -0.707 and the same is in sin (hr18 – 13.5). The main disadvantage of this model is that it requires many input parameters that may be available only for researchers, not for practitioners



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2.2 Asphalt Institute Model

The Asphalt Institute (AI) model [The Asphalt Institute 1982] relates the mean pavement temperature, Tp, and the mean monthly air temperature, Ta , by the following simple equation:

64

34

4

11 +

+−⎟

⎠⎞

⎜⎝⎛

++=

zzTT aP

(2) where Tp = Mean pavement temperature at depth Z, oC; Ta = Mean monthly air temperature, oC; Z = depth from surface, mm.

2.3 The IPAT (Idaho Pavement Temperature) Model

Based on LTPP data and temperature data collected at the state of Idaho, a regression model has been developed to relate asphalt pavement temperature to the air temperature and thermal history. The regression analysis led to the following equation [Abo-Hashema and Bayomy 2002]:

0314.00806.01261.0 *3109.5**2041.0**5932.1 −− ++= ZZTZTT maP (3)

where Tp = Pavement temperature at depth Z, oC; Ta = Air temperature, oC; Tm = Thermal history, which is defined as the average air temperature calculated during the 24 hours preceding the time at which the pavement is tested, oC; Z = Depth from surface, mm (must be greater than zero) This equation represents the Idaho Pavement Temperature (IPAT) model. The R2 of the regression Equation (3) is 0.955 and the standard error of estimate (SEE) is 1.85 oC. Since the data used in this analysis were for mid-depth pavement temperature. Equation (3) is not valid for Z =0, which means that it cannot be used to predict the pavement surface temperature (i.e. at Z =0) [Abo-Hashema and Bayomy 2002].

2.4 LTPP High & Low Pavement Temperature Models

The LTPP models have empirical nature and are developed from LTPP seasonal monitoring by Mohseni & Symons [Mohseni and Symons 1998]. These models relate pavement temperatures (low and high) to air temperature, latitude, and depth, as follows: High Pavement Temperature Model

( ) ( ) 5.02air10

2air S 61.0925log 14.15Lat 0025.0T 78.032.54 +++−−+= zHTpav (4)

where Tpav = High AC pavement temperature below surface, oC; Tair = High air temperature, oC; Lat = Latitude of the section, degrees; H = Depth to surface, mm; Sair = Standard deviation of the high 7-day mean air temperature, oC; z = Standard normal distribution table, z = 2.055 for 98% reliability. The R2 value of that model is 0.76 and SEE is 3.0 based on 309 data points [Mohseni and Symons 1998].



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Low Pavement Temperature Model

( ) ( ) 5.02air10

2air S 52.04.425log 26.6Lat 004.0T 72.056.1 +−++−+−= zHTpav (5)

where Tpav = Low AC pavement temperature below surface, oC; Tair = Low air temperature, oC; Lat = Latitude of the section, degrees; H = Depth to surface, mm; Sair = Standard deviation of the mean low air temperature, oC; z = Standard normal distribution table, z = 2.055 for 98% reliability. The R2 value of that model is 0.96 and SEE is 2.1 based on 411 data points [Mohseni and Symons 1998].

2.5 A Simple Asphalt Pavement Temperature Model (Idaho Study)

An effort was recently made to relate the asphalt pavement temperature to the air temperature for different LTPP sites. Data from eight different sites were included in this analysis; five from non-freezing zones and three from freezing zone. The parameters incorporated in the prediction of the AC temperature were the air temperature at the time of testing, the month and the depth at which it is required to predict the AC temperature, and the site latitude to represent the solar radiation. The month number was included in a sinusoidal function because the difference between air and pavement temperatures is greatest during summer and winter while during spring and fall the temperature difference is small [Bayomy and Salem 2004]. Regression analysis was employed to predict the asphalt pavement temperature from the previously stated parameters using the SAS program, and the result is shown Equation (6). The asphalt pavement temperature could be predicted with R2 value of 0.954 and root MSE of 2.6 [Bayomy and Salem 2004].

( ) ( )[ ] 956.8 00396.0 398.025.1log2709.06

716.06075.0 210 +−+

⎭⎬⎫

⎩⎨⎧ −−⎥⎦

⎤⎢⎣⎡ ∗−∗+= LatTZMCOSTT sairac

π

(6) where Tac = Asphalt pavement temperature, oC; Ts = Asphalt surface temperature recorded during FWD test, oC; Tair = Air temperature, oC; Z = Depth at which it is intended to predict the AC temperature, mm; M = Month number (1, 2,……..,12) Lat = Latitude, Degree Although all the model parameters used to predict the AC pavement temperature in Equation (6) are significant, there may be a concern that the asphalt surface temperature might not be available in some sites. Therefore, it is excluded from the model to simplify the model input parameters and make it applicable to all sites. The analysis of variance (ANOVA) and the parameter estimates for the reduced model were performed. The reduced model is shown in Equation (7), which has R2 value of 0.932 and root MSE of 3.156 [Bayomy and Salem 2004].

( ) ( )[ ] 627.8 0035.025.1log2618.06

71779.0045.1 210 +−

⎭⎬⎫

⎩⎨⎧ −−⎥⎦

⎤⎢⎣⎡ ∗−∗+= LatZMCOSTT airac

π (7)



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3. ARTIFICIAL NEURAL NETWORKS

3.1 Neural Network Theory

It is not necessary to know the details of neural networks in order to use them, but this basic introduction can be helpful. A complete coverage of neural network theory can be found in many references such as a book by Principe et al. [Principe et al. 2000].

3.1.1 Neural Network Definition A neural network is an adaptable system that can learn relationships through repeated presentation of data and is capable of generalizing to new, previously unseen data. Some networks are supervised, in that a human determines what the network should learn from the data. In this case, users give the network a set of inputs and corresponding desired outputs, and the network tries to learn the input-output relationship by adapting its free parameters. Other networks are unsupervised, in that the way they organize information is hard-coded into their architecture [Lefebvre et al. 2005]. Neural network architectures, arranged in layers, involve synaptic connections amid neurons that receive signals and transmit them to the others via activation functions. Each connection has its own weight and learning is the process of adjusting the weight between neurons to minimize error between the calculated and predicted values. In Figure 1, a typical structure of ANN is presented. It consists of a number of neurons that are usually arranged in layers, which are the input layer, hidden layers, and output layers [Bayrak et al. 2005]

Figure 1. A Typical Architecture of ANN.

3.1.2 Neural Network Use Neural networks are used for both regression and classification. In regression, the outputs represent some desired, continuously valued transformation of the input patterns. In classification, the objective is to assign the input patterns to one of



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several categories or classes, usually represented by outputs restricted to lie in the range from 0 to 1, so that they represent the probability of class membership. For regression, a single hidden layer or Multilayer Perceptron can learn any desired continuous input-output mapping if there are sufficient numbers of axons in the hidden layer(s) [Lefebvre et al. 2005].

3.2 Neural Network Software Packages

There are many available neural network software packages. In this study, NeuroSolutions software, version 5.06, has been used as a tool in designing and training a neural network. In the NeuroSolutions software, there is a wizard tool taking the user through the process of designing and training a neural network. Neural networks can be very powerful learning systems. However, it is very important to match the neural architecture to the problem. The Neural-Builder of the NeuroSolutions software constructs the most popular neural architectures. However, Multilayer Perceptron (MLP) model is considered the most widely used neural network. MLPs are layered feed forward networks typically trained with static back propagation. These networks have found their way into countless applications requiring static pattern classification. Their main advantage is that they are easy to use, and that they can approximate any input/output map. The key disadvantages are that they train slowly, and require lots of training data. Detailed description about this software can be found in the references [Lefebvre et al. 2005].

4. OVERVIEW OF LTPP PROGRAM

In 1984, the Strategic Transportation Research Study was initiated. Its focus was to develop a research agenda that would produce major innovations for increasing the productivity and safety of the Nation’s highway system. One component of this effort was the Long Term Pavement Performance program, a 20-year study of in-service highway pavements [DataPave3.0 2001]. Planning for the LTPP program began in 1985. It was a cooperative effort of American Association of State and Highway Transportation Officials (AASHTO), the National Cooperative Highway Research program (NCHRP), the Transportation Research Board (TRB), and the Federal Highway Administration (FHWA). In 1987 with the passage of the Surface Transportation Assistance Act, LTPP was launched as part of the Strategic Highway Research Program (SHRP). After the first five years were completed under SHRP, the LTPP program became an FHWA-managed effort in July 1992 [DataPave3.0 2001]. The LTPP program has two complementary experiments to meet the objectives. The General Pavement Studies (GPS) use existing pavements as originally constructed or after the first overlay and focus on the most commonly used structural designs for pavement. The second set of LTPP experiments is the Specific Pavement Studies (SPS). The SPS test sections allow critical design factors to be controlled and performance to be monitored from the initial date of construction [DataPave3.0 2001].



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To study the environmental effect on pavement structures, there is a sub-program called Seasonal Monitoring Program (SMP) within the LTPP program. The primary objective of the SMP is to provide information on variations in temperature and moisture content within a pavement structure. Limited resources make it impossible to obtain detailed climatic impacts on all of the sections. To obtain the maximum benefits from available resources sixty-four sites were selected as the core group. GPS and SPS sites are included. The sites were divided into two groups. Each group was intensively monitored in alternate years. Climatic data was collected continuously throughout that year. Monitoring of pavement strength was conducted monthly during the year. Measurements of surface characteristics were obtained at least seasonally during the year. That information will allow pavement engineers to design better, longer-lasting roads, and to provide answers to HOW and WHY pavements perform as they do [DataPave3.0 2001]. These data are housed in an Information Management System (IMS). By the completion of the LTPP study, the LTPP-IMS is expected to become the world's largest pavement performance database, with enormous potential for the development of products to improve pavement technology [DataPave3.0 2001]. The DataPave3.0 software is a tool to explore, review, and retrieve information from the massive LTPP database. Using various filters and criteria, users can obtain information from a selected number of pavement sections in the database. DataPave3.0 is fast, easy to use, and provides information in a format that is easy to read and understand [DataPave3.0 2001].

5. ANN-BASED PAVEMENT TEMPERATURE PREDICTION MODEL

5.1 Analysis Methodology

In order to develop an ANN-based pavement temperature prediction model, it is necessary first of all to have a database of measured pavement temperature with some other related parameters. For this reason, some LTPP-SMP sites have been selected using DataPave3.0 software. Pavement temperature data and some other related data have been obtained for the selected sites to create pavement temperature database. Training data sets were then selected to be used in a training process for ANN approach. Two groups of training data sets have been created. NeuroSolutions 5.0 software, version 5.06, was used in designing and training the neural network. Sensitivity analysis on the trained ANN has been also conducted. Finally, a testing or validating process was performed on the two groups of trained ANN. Figure 2 presents the analysis methodology steps adopted in this study divided into the following four main steps:

• Selected LTPP sites • Development of pavement temperature database • Training process • Sensitivity analysis on the trained ANN • Validating process



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Selected LTPP Sites

Training Process

Pavement TemperatureDatabase

Trained ANN

AccuracyRate

Four DifferentClimatic Zones

LTPPDataPave3.0

Software

ValidatingProcess

Other TrainingSets

ANN Software

High

Implement Low

Type of Transfer FunctionNo. of Hidden NodesNo. of Hidden Layers

ValidatingSets Training

Sets

SensitivityAnalysis

Selected LTPP Sites

Training Process

Pavement TemperatureDatabase

Trained ANN

AccuracyRate

Four DifferentClimatic Zones

LTPPDataPave3.0

Software

ValidatingProcess

Other TrainingSets

ANN Software

High

Implement Low

Type of Transfer FunctionNo. of Hidden NodesNo. of Hidden Layers

ValidatingSets Training

Sets

SensitivityAnalysis

Figure 2. Analysis Methodology.

5.2 Selecting LTPP Sites

Eleven LTPP-SMP sites were selected to represent each climatic region of flexible pavements. The LTPP sites locations and identifications are presented in Table 1. Table 1. LTPP Sites Locations and Identifications Climatic Region: Wet Freeze Site ID Exp.

No. State and SHRP Region AC Thicknesses

9-1803-1 GPS1 Connecticut (CT), North Atlantic 198 mm 23-1026-1 GPS1 Maine (ME), North Atlantic 162 mm 24-1634-1 GPS2 Maryland (MD), North Atlantic 91.4 mm 25-1002-1 GPS1 Massachusetts (MA), North Atlantic 198.1 mm Climatic Region: Dry Freeze 16-1010-1 GPS1 Idaho (ID), Western 271.8 mm 30-8129-1 GPS1 Montana (MT), Western 76.2 mm Climatic Region: Wet No Freeze 13-1005-1 GPS1 Georgia (GA), Southern 195.6 mm 28-1016-1 GPS2 Mississippi (MS), Southern 55.9 mm 48-1077-1 GPS1 Texas (TX), Southern 51 mm Climatic Region: Dry No Freeze 4-1024-1 GPS1 Arizona (AZ), Western 274 mm 35-1112-1 GPS1 New Mexico (NM), Southern 160 mm

5.3 Development of Pavement Temperature Database

Pavement temperature database has been created to be used in designing and training a neural network. The database contains the following data:

• Depth from surface (mm), Z, at which the pavement temperature is tested • Air temperature (oC), Ta



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• Thermal history (oC), Tm, which is defined as the average air temperature calculated during the 24 hours preceding the time at which the pavement is tested

• Infrared surface temperature (oC), IR • Measured pavement temperature (oC), Tp, at depth Z.

More than 700 readings/cases in various months and depths for the selected sites have been obtained from the DataPave3.0 software. Table 2 shows a sample of some selected readings or cases captured from the developed database. It is noteworthy that the measured pavement temperature, Tp, is the desired output.

5.4 Training Process

In order to develop ANN-based pavement temperature prediction model, it must be well trained using training sets extracted from the developed database. Therefore, 630 cases have been selected from the created database to represent training sets. The data of the training sets contain depth, air temperature, thermal history, infrared surface temperature, and pavement temperature. These training sets were named as the first group. A second group of training sets has been also created using the same 630 cases but containing only measured asphalt pavement temperature of various depths and air temperature. The reason for creating a second group is to investigate the relationship between only pavement and air temperatures. This second group becomes important to the ordinary site engineer because some other data parameters of the first group might be unavailable. The NeuroSolutions software has been used in the training process. Table 2. Selected Cases from Developed Database

Depth (Z), mm

Air Temperature (Ta),

oC Thermal History

(Tm), oC Infrared Surface Temperature

(IR), oC Measured Pavement Temperature (Tp),

oC 25 -11.7 -8.5 -1.9 -7.6 25 -6.1 -9.4 -1.4 -4.3 25 -4.8 -6.1 -2.1 -3.7 25 23.8 23.5 43.4 34 25 24.2 23.8 42.6 34 89 -7.6 -6.8 -6 -4.2 89 6.9 1.7 14.3 3.7 89 22.1 21.7 42.6 28.7 70 -0.8 -4 -4.2 -0.6 70 25.2 23 46.3 33 23 16.8 18 35.4 28.4

137 16.8 18 35.4 25.7 137 24.2 22.6 49.1 34.4 25 30.8 30.8 45 39.1 25 28.4 27.2 44.1 37.3

The Neural-Builder of the NeuroSolutions Software only accepts column-formatted ASCII files. After loading the two groups of training data sets, the Neural-Builder will scan the files and present a list of the columns that it finds. Initially all columns will be tagged as inputs. User can tag a column as either "Input", "Desired", "Symbol", "Annotate" or "Skip". To change a columns tag,



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simply select the column with the mouse and press the corresponding button. In this analysis, the last column “Tp”, pavement temperature, was tagged as “Desired”. The number of hidden layers, hidden nodes, and transfer function should be specified. In this study, two hidden layers, 25-hidden nodes, and TanhAxon transfer function were selected. The problem is to find the best mapping from the input patterns to the desired response (Tp). The neural network will produce from each set of inputs a set of outputs. Given a random set of initial weights, the outputs of the network will be very different from the desired classifications. As the network is trained, the weights of the system are continually adjusted to incrementally reduce the difference between the output of the system and the desired response. This difference is referred to as the error and can be measured in different ways. The most common measurement is the Mean Squared Error (MSE). The MSE is the average of the squares of the difference between each output and the desired output. Training results indicated that the MSE of the first group is equal to 0.005. On the other hand, the second group produces the MSE of 0.012, which is considered 2.4 times higher than the first group. However, the MSE of the second group is considered acceptable, while the MSE of the first group is considered superior.

5.5 Sensitivity Analysis

The objective of the sensitivity analysis is to express the fitness of neural networks as an effective way in predicting the asphalt pavement temperature with the most achievable accuracy. The neural networks were influenced to several parameters that can guarantee the greatest achievable accuracy such as type of transfer function, number of hidden nodes, and hidden layers. Figure 3 shows the analysis results with different parameters.

94

95

96

97

98

99

100

0 20 40 60 80 100 120

%A

ccu

racy

No. of Nodes

Tanh Function-One Hidden Layer Tanh Function-Two Hidden LayersSigmoid Function-One Hidden Layer Sigmoid Function-Two Hidden Layers Figure 3. Results of Sensitivity Analysis of ANN

The analysis indicates that changing the transfer function has a noticeable effect on the accuracy, where using the Tanh function is much better than using the Sigmoid function. Furthermore, the Tanh function is much interacting with number of nodes than Sigmoid function. For example, using the Tanh function achieves average 1.55% more in accuracy than the Sigmoid function.



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Furthermore, the number of hidden nodes has an effect on the accuracy, where using more number of hidden nodes gives high accuracy. To achieve high accuracy, the number of hidden nodes is preferable to be more than 25 nodes. On the other hand, NeuroSolutions predicts much better with the two hidden layers

5.6 Validating Process

Once the network has been trained, validating process should start using testing data sets selected from the created database. The trained network should not be exposed to these data sets before. Therefore, 60 different cases have been selected to represent validating data sets. The predicted pavement temperatures of these 60 cases using the two trained networks of the two groups were compared with the corresponding measured ones to come up with the accuracy rate or reliability. If the accuracy rate is low, then the network is not properly trained and other training sets should be generated to retrain the network. Otherwise, the network is considered to be reliable and ready for implementation Validating process has been performed for the two trained networks of the two groups. Table 3 shows an example of some selected results comparing between the measured and predicted asphalt pavement temperature as well as the corresponding accuracy rate for the two groups. The average accuracy rate for the 60 cases is 81% and 72% for the first and second groups, respectively. Although the average accuracy rate of the two groups are considered not very high, more than 60% of the testing cases have accuracy rates over 90% for the first group. On the other hand, 50% of the testing cases have accuracy rate over 90% for the second group. Finally, while the first group is more accurate than the second group, the accuracy rate of the second group is considered acceptable.

6. ANALYSIS OF THE RESULTS

The results of predicted asphalt pavement temperatures for the two groups were fitted to the measured corresponding data collected from LTPP-SMP sites, and the results are shown in Figure 4. The figure shows the following points:

• For the first group: the data are well centered around the equity line and the trend line is identical on the equity line, which indicates that the ANN model for the first group fits the data very well.

• For the second group: the data tends to be underestimating the asphalt

pavement temperature when the temperature is over 10 oC, while it tends to be a slight overestimating when the temperature is below 10 oC. This explanation can be seen by the trend line of the second group.

• Generally, the trained network of asphalt pavement temperature gave a

very close estimation to the measured values for both two groups of training data sets



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Table 3. Sample of Results for the Two Groups of Training Sets Measured Pavement

Temperature from LTPP (Tp),

oC

Predicted Pavement Temperature using Trained Neural Network Accuracy Rate, %

First Group Second Group First Group Second Group

-6.2 -3.33 -5.28 53.71 85.16 -0.7 -0.46 0.09 65.71 12.86 33.5 34.26 33.08 97.78 98.75 0.5 0.5 3.12 100.00 16.03 0.2 1.4 1.75 14.29 11.43 8.5 2.21 6.2 26.00 72.94

27.4 29.69 28.88 92.29 94.88 35.3 34.67 28.88 98.22 81.81 28.8 29.04 29.26 99.17 98.43 31.4 32.41 29.17 96.88 92.90 28.2 29.81 28.88 94.60 97.65 22.1 22.68 23.5 97.44 94.04 32.1 30.65 24.83 95.48 77.35 32.8 31.42 27.39 95.79 83.51 39.9 35.25 30.87 88.35 77.37 0.4 -2.11 1.64 18.96 24.39 -1.8 -4 0.42 45.00 23.33 -1.6 -4.31 -0.06 37.12 3.75 -2 -4.78 -1.73 41.84 86.50

-3.1 -5.11 0.92 60.67 29.68 -3.7 -5.65 -3.43 65.49 92.70 20 21.04 19.51 95.06 97.55

18.3 20.3 17.42 90.15 95.19 19.9 20.56 17.05 96.79 85.68 23.5 23.74 21.19 98.99 90.17 26.6 26.3 24.14 98.87 90.75 31.8 29.91 29.6 94.06 93.08 31.7 30.17 30.27 95.17 95.49 33 30.67 30.36 92.94 92.00

32.1 30.42 30.6 94.77 95.33 30.3 28.79 30.27 95.02 99.90 30.5 30.17 30.27 98.92 99.25 30.3 30.11 28.82 99.37 95.12 32.2 32.83 34.17 98.08 94.23 14.5 19.57 16.94 74.09 85.60 15.4 15.57 19.76 98.91 77.94

Furthermore, the 60 testing data sets have been plotted against the measured and predicted asphalt pavement temperatures to show fluctuations of the predicted values with respect to the measured ones, as shown in Figure 5 for the first group and Figure 6 for the second group.



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-10

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20

30

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50

-10 0 10 20 30 40 50Measured Pavement Temperature (LTPP), oC

Pre

dic

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Pav

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N),

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First Group, All Data

Second Group, only Air Temp.

Equality Line

Linear (First Group, All Data)

Linear (Second Group, only Air Temp.)

Figure 4. Measured versus Predicted Asphalt Pavement Temperatures for

the two Groups of Training Sets.

-10

0

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20

30

40

50

0 10 20 30 40 50 60

Number of Training Sets

Pav

emen

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per

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Measured

First Group, All Data

Figure 5. Fluctuations between Measured and Predicted Asphalt Pavement

Temperatures for the First Group of Training Sets.

-10

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20

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40

50

0 10 20 30 40 50 60

Number of Training Sets

Pav

emen

t Tem

per

atu

re, C

Measured

Second Group, only Ta

Figure 6. Fluctuations between Measured and Predicted Asphalt Pavement

Temperatures for the Second Group of Training Sets.



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A correlation analysis was also made between the measured and predicted asphalt pavement temperatures for the two groups with test of significant 2-tailed. A two-tailed significance is the probability of obtaining results as extreme as the one observed in either direction when the null hypothesis is true. It tests a null hypothesis in which the direction of an effect is not specified in advance. This correlation analysis is to show how strong the relationship between the measured and predicted temperatures is. The results indicate the following:

• For the first group: the correlation coefficient is 0.985 with Standard Error of Estimate (SEE) 1.30oC.

• For the second group: the correlation coefficient is 0.965 with SEE 2.34oC.

Results indicate that the relationship between the measured and predicted asphalt pavement temperatures is strong with acceptable SEE for both two groups. Although the first group gives results much more accurate than the second group, the ANN-based asphalt pavement temperature model of the second group is preferable to be used. The reason for that is to make it easy in use for the ordinary engineer as well as in case of air temperature is only available. Finally, ANN can be effectively used to predict asphalt pavement temperature.

7. CONCLUSIONS

In this study, Artificial Neural Network-based (ANN) asphalt pavement temperature prediction models have been developed. The neural network has been trained using data extracted from the Long Term Pavement Performance (LTPP) program - DataPave3.0 software. The training and validating processes have been conducted using NeuroSolutions software. Two ANN models have been developed. The first model is to predict asphalt temperature based on air temperature along with some other related temperature parameters such as thermal history and infrared surface temperature. Second model deals with only air temperature in predicting the Asphalt Concrete (AC) temperature for simplicity to the ordinary practitioner. Results of this study reveal that ANN is appropriate for implementation in predicting asphalt pavement temperature. In addition, using only air temperature in predicting AC temperature gives acceptable results. This is particularly promising for developing countries where such applications can play an effective role in the light of unavailability of some input data parameters.

REFERENCES

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Stubstad, R. N., S. Baltzer, Erland O. Lukanen and H. J. Ertman-Larsen (1994). “Prediction of AC Mat Temperatures for Routine Load/Deflection Measurements” Proceedings of 4th International Conference on the Bearing Capacity of Roads and Airfields, Trondheim, pp. 401-412.

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