Dynamic Artificial Neural Networks for Dowel Bending ...

Dynamic Artificial Neural Networks for Dowel Bending Moment Prediction from Temperature Gradient Profile in Concrete Slabs Adel W. Sadek, Ph.D.* Assistant Professor Department of Civil and Environmental Engineering University of Vermont Burlington, VT 05405 Phone: (802) 656-4126 FAX: (802) 656-8446 E-mail: [email protected] Samir N. Shoukry, Ph.D. Professor Departments of Mechanical & Aerospace Engineering and Civil & Environmental Engineering West Virginia University 517 Engineering Sciences Building Morgantown, WV 26505 (304) 293-3111 ext. 2367 FAX (304) 293-6689 E-mail: [email protected] & Mourad Riad Engineering Scientist Department of Civil & Environmental Engineering West Virginia University 115 Engineering Sciences Building Morgantown, WV 26505 (304) 293-3111 ext. 2613 FAX (304) 293-6689 E-mail: [email protected]

Transportation Research Board 82nd Annual Meeting Washington, D.C. *

Corresponding Author

Word Count: 4678 words + (11 Figures) = 7428 equivalent words

TRB 2003 Annual Meeting CD-ROM

Original paper submittal – not revised by author.

ABESTRACT Wide spread use of neural networks in mechanistic pavement analysis has been limited due to lack of sound experimental data that relate input variables such as temperature and traffic loading to quality–measured mechanical response parameters. In this paper, data collected from an instrumented section of Robert C. Byrd's Highway (Route 33) near Elkins, West Virginia, is used to test the potential of two classes of dynamic artificial neural networks (ANNs) in predicting the bending moment induced in shoulder side dowel. At any time instant, this bending moment expresses the extent of concrete slab curvature caused by construction factors, moisture gradient, and in-service temperature gradient through the slab thickness. The two classes of ANNs examined in this study are: (1) Time Delay Neural Networks (TDNN); and (2) Elman/Jordan Networks, The input to the networks is the time-history of the measured temperature gradient profile (TGP) through the thickness of the slab. Results from this study show that dynamic ANNs are quite capable of capturing the relationship between the time-history of the TGP and the dowel bar bending moment. The results also indicate that Elman/Jordan networks slightly outperformed TDNNs for the problem considered in this study. KEY WORDS Neural networks, dowel bar, bending moment, instrumented pavements.



Sadek, Shoukry and Riad

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Dynamic Artificial Neural Networks for Dowel Bending Moment Prediction from Temperature Gradient Profile in Concrete Slabs

INTRODUCTION Currently, wide spread use of Artificial Neural Networks (ANNs) in mechanistic pavement analysis is still somewhat limited due to the lack of sound experimental data that relate input variables such as temperature and traffic loading to quality–measured mechanical response parameters. While this is the case, the transportation literature, nevertheless, contains several examples of the use of ANNs for different aspects of pavement performance analysis. For example, Lee and Lee (1) developed Neural Network Algorithms for pavement crack analysis. Shekharan (2) used ANNs to assess the relative contribution of input variables on pavement performance prediction. Ceylan et al. (3) used ANNs to capture the results of more than 38,000 ILLI-SLAB finite element analyses runs performed on a four-slab airfield pavement system. Abdelrahim and George (4) developed ANNs for pavement maintenance strategy selection. Martinelli and Shoukry (5) used ANNs to identify concrete specimens that contain internal cracks. Lou et al. (6) developed ANN models for forecasting pavement crack condition. While this is by no means a comprehensive listing of the applications of ANNs to pavement modeling and analysis, a common observation is that, in the majority of these previous studies involving ANNs and pavement modeling, the ANN topology used was the simple Multi-layer Perceptron (MLP) network, which is mainly suited for static mappings. In the current paper, shoulder side dowel bending moment, measured on a recently instrumented section of Robert C. Byrd's Highway (Route 33) near Elkins in West Virginia, is used to develop two different classes of dynamic neural networks that predict the Dowel-Bending Moment (DBM) given the measured Temperature Gradient Profile (TGP) through the thickness of 11 in. concrete slab. DBM is measured using proprietary instrumentation technology that enables continuous measurement of DBM without interruption. Both DBM and TGP are collected every 20 minutes for duration of 250 days starting from the instant of concrete casting. There are at least two features that distinguish this study from other papers in the area of ANNs and pavements. First, this study uses dynamic ANNs, that are better equipped for time series modeling, as opposed to the standard MLP commonly used in previous studies. Secondly, the study uses an extensive, real-world data set for developing the ANNs, and not merely finiteelement simulation results. The paper is organized as follows. First the significance of DBM estimation is discussed. This is followed by a description of the instrumented test bed and of how the DBM is measured. Next, ANNs are introduced, and the difference between static and dynamic modeling is discussed. The two different classes of dynamic ANNs are then developed, and their performance is evaluated. The paper concludes by summarizing the major conclusions derived from the study.




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SIGNIFICANCE OF DOWEL-BENDING MOMENT ESTIMATION In concrete pavements, built-in curvature, warping, and curling are induced due to temperature gradient at the time of construction, moisture gradient, and in-service temperature gradient through the thickness of a concrete slab. Together they cause concrete slabs to be slightly curved into convex or concave shape. This curvature is caused by large magnitude stresses that are known to be major contributors to various forms of damage including transverse joint distress and mid slab cracking (7, 8). Due to thermo-mechanical properties of concrete material, changes in ambient air temperature induce corresponding changes in the Temperature Gradient Profile (TGP) through the thickness of a concrete slab (9, 10). Using nonlinear Three-Dimensional Finite Element (3DFE) modeling it is possible to mechanistically investigate the effect of TGP on slab curling (11). Dowel bars (18 in long steel rods) are used in plain concrete pavements to transfer axle load across transverse joints thus improving the rid quality. As the slab curvature changes, the dowels across adjacent slabs bend accordingly (12). Figures 1(a) and (b) illustrate a 3DFE modeling of concrete slab response to negative and positive TGP respectively. The figures illustrates that bent dowels follow the way the slab curvature changes. Dowel bending moment can produce early age cracking at transverse joints (13). It has also been shown that dowel bending may cause mid slab cracking (14). In an attempt to understand the relation between slab curvature and mid-slab cracking, the Federal Highway Administration funded research to explore the possibility of establishing a correlation between concrete pavement distress and slab curling and warping profile as measured using non-contact high speed profiler (15). Although such measurement has the advantage of being performed on a large number of slabs, it is: a) costly, b) not suitable for continuous monitoring of curvature changes over short time intervals, c) the sensitivity of slab profile change to a change in TGP is unknown, and d) cannot be performed on concrete during the curing stage. Alternatively, Figure 1 indicates that dowel bar bending moment can be taken as a direct measure of the extent of slab curvature at any time. The primary advantage of measuring Dowel-Bending Moment (DBM) is the ability to obtain a continuous record over the pavement life (20 or more years) sampled at every few minutes. Together with continuous measurement of TPG, DBM cold be used to study how slab curvature is influenced by concrete mix design, construction curling, moisture warping as well as the response to ambient temperature variations.

INSTRUMENTED HIGWAY In August 2001, West Virginia University researchers instrumented 450 ft long section of a newly constructed dowel jointed concrete pavement along Robert C. Byrd's highway (Route 33) near Elkins, West Virginia, USA. One of the project objectives is to provide reliable field data that could be used to validate the thermal and mechanical responses of 3DFE models of dowel jointed concrete pavements (11, 12). The data will also be used to develop and test the performance of several computational intelligence (CI) techniques to predict various mechanistic pavement response parameters from traffic and environmental loading information, which is the topic of this paper.




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The instrumented section, Figure 2 (a) and (b), consists of 30 dowel jointed concrete slabs, each 28 cm (11 in.) thick, 4.6 m (15 ft) long, and 3.6 m (12 ft) wide. The slabs are placed on top of a 10 cm (4 in.) asphalt-stabilized, free-drainage base constructed over 15 cm (6 in.) compacted gravel. To ensure uniform and minimal slab-base friction, the base was covered with approximately 1 cm thick layer of coarse sand that filled the surface voids of the free-drainage base prior to concrete placement. In total, six of the 30 slabs along the section were fitted with systems of sensors designed for continuous monitoring of TGP, longitudinal and transverse strains, dowel bar bending moments induced due to slab curling and warping, and joint-meters for monitoring transverse and longitudinal joints openings. Figure 2(a) illustrates the sensors installed in a typical instrumented slab prior to concrete placement. Acquisition of data from all sensors started few minutes before the concrete placement and continues to date at a rate of one reading every 20 minutes. Details of the instrumentation plans and methods of data collection were discussed elsewhere (Shoukry 2002). Figure 3 illustrates the time history of measured temperatures at nine vertically aligned points through the thickness of the slab. Figure 4 illustrates the magnitude of temperature gradient (described by the difference between slab top and bottom temperatures) in the slab that developed during the monitoring period. Over the monitoring period of 250 days (from September 2001 to May 2002), the difference between slab top and bottom temperatures varied between –8ºC to +11ºC.

DOWEL BENDING MOMENT MEASUREMENT At any time instance through the life of a concrete slab, the total slab curvature is produced by the combined effect of major parameters: shrinkage, construction curling, moisture gradient, slab-base friction, dowel-concrete friction in addition to the in-service TGP. Due to geometrical and material nonlinearity, the dowel-bending component raised by each factor is nonlinear with temperature, and is time dependent. Thus, at any time instant, that total dowel bending moment induced is the sum of bending moments induced by slab curvature due to all of the above factors. DBM has been measured in the past using wire resistance strain gauges that require zeroing of the gage readings before any measurement is made for a short duration of time that may extend from few minutes to 24 hours. Over the period of measurement using wire resistance gauges, the measured values suffer from gradually increasing error produced by electronic drift in the measuring system. Thus, wire resistance gauges cannot be used for long term monitoring (several years) of dowel bar bending. The instrumented dowel used in measurement of DBM is a standard epoxy coated dowel fitted with bending moment sensing element as shown in Figure 5(a). DBM is computed from the change in frequency that occurs in the sensing element. The measuring system does not require zeroing allowing uninterrupted, continuous recording of DBM from the time of concrete casting. The bending moment readings from the instrumented dowel were carefully calibrated at WVU laboratories using four-point bending test illustrated in Figure 5(b). Because frequency is measured, the sensor readings are unaffected by cable length. An innovative mean of wiring and connecting the sensors provided moisture-proof protection without any alteration of the




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cylindrical form of the dowel. The instrumented dowel is mounted in the pavement using standard dowel baskets used to mount standard dowels as illustrated in Figure 5(c). Figures 6(a) illustrates the time history of the DBM induced in the shoulder side dowel from the instant of concrete casting. Figure 6(b) is a blow up of the bending moment history plot illustrating that the instrumented dowel produced noise-free readings. Twelve such instrumented dowels were used along the instrumented highway to monitor DBM at various locations along the transverse joints of different slabs. All instrumented dowel continue to function efficiently eleven months after construction. Figure 6(c) illustrates the ambient temperature time history during the same period for which the dowel bending moment data is shown in Figure 6(a). In this paper, we will develop and test two neural networks to predict the dowel bending as shown in Figure 6 from the temperature gradient profile shown in Figure 3.

ARTIFICIAL NEURAL NETWORKS AND FUNCTION APPROXIMATION ANNs are biologically-inspired systems consisting of a massively connected network of computational “neurons”, organized in layers. Starting from the pioneering work of Rosenbalt (16), along with Minsky and Pappert (17), NNs have evolved into what is today regarded as an important reservoir of learning methods and architectures that can serve as excellent function approximators (18). Given a set of input vectors x and a set of desired response d, and assuming that the desired response d is an unknown but fixed function of the input d = f(x), the goal in the function approximation problem is to learn or discover the function f(.) from a finite set of inputoutput pairs (x, d). ANNs do this by adjusting the network’s weights connecting the “neurons” (w) so that the network’s output, y = f^(x, w) would give the desired response (Figure 7). A number of learning algorithms (such as the famous back propagation algorithm) could be used to adjust the weights of the network based upon the error signal resulting from the difference between the desired output, d, and the ANN output, y, in a type of learning that is commonly referred to as supervised learning. It has been shown that ANNs are universal function approximators, which means that they are capable of approximating any continuous function, provided that enough “neurons” are used (19). Static versus Dynamic Modeling While many possible classifications are available for the different types of ANN architectures, in this paper, we distinguish between static networks, and dynamic networks. Static problems do not involve time, and for those types of problems, the famous Multi-layer Perceptron (MLP) NN is quite adequate. The MLP typically consists of three or more layers of neurons: the input layer, the hidden layer(s), and the output layer. The type of connections in the MLP is of the feedforward type. For dynamic problems, on the other hand, time establishes an order in the input data, and provides an extra structure in the input space that should be exploited by a modeling tool. For a modeling tool, however, to be able to take advantage of this extra structure, the tool has to have short-term memory to allow it to remember the past values of the data.




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In dynamic ANNs, there are different methods by which this short-term memory could be implemented. One method involves the use of a tap delay line. A delay line is a single input, multiple-output system built from a cascade of ideal delay elements, where each element is a linear system, denoted by z-1, which delays the input signal by one sample. For example, if (n-1) delays are cascaded together, the system will have access to the present sample, along with the past (n-1) samples. Another method of implementing short-term memory in ANN is through the use of recurrent/feedback connections. For these systems, the output at time n depends not only on the input, but also on the output at a previous time, as, for example, given by the following equation: y(n) = (1 – µ) . y(n-1) + x(n)

Equation 1,

where y(.) is the output, x(.) is the input, and (1 – µ) is called the feedback coefficient. As can be seen, recurrent systems have an infinite impulse response, as opposed to a tap delay line, which has a finite response defined by the number of delay elements. Several topologies of dynamic ANNs, built on the concepts just described, are available. In the following sections, we describe two of the most important of these topologies, which were utilized in this study to develop ANNs for predicting DBM from TGP. Time Lagged Neural Network (TLNN) TLRNs are MLPs extended with short term memory structures that have local recurrent connections. The memory structures could be of the tap delay line type, resulting in what we call Time Delay Neural Networks (TDNN). They could also be of the recurrent type or what we call memory by feedback or context Processing Elements (context PE) type. The use of context PEs allows for increasing the memory depth (i.e. how long a given value is remembered) without any topological modifications (i.e. by changing the value of the feedback parameter, µ). This is unlike the case of the delay line type. A special type of TLNN is what we call the focused topology, which only includes the memory structures in the input layer. A focused TDNN can be trained with the standard back propagation algorithm. For the other topologies, a special learning algorithm known as back propagation through time (BPTT) is used. BPTT is much more complex than the standard back propagation algorithm. Elman and Jordan Networks The Elman and Jordan networks are based on combining MLPs with context PEs and network recurrency. In the Elman network, the output of the hidden PEs from the previous time step are copied to the context units (Figure 8). In the Jordan network, the output of the network is copied to the context units. In addition, the context units feedback on themselves (i.e. are locally recurrent). The local recurrence decreases the values by a multiplicative constant τ, which determines the memory depth.




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The Elman and Jordan systems are, in principle, more efficient than the focused architectures for encoding temporal information, since the memory is “inside” the network, and not just at the input layer. One disadvantage of the Elman and Jordan networks, however, is that they have fixed feedback parameters. The feedback parameters are fixed in the Elman and Jordan networks to allow for their training using the standard back propagation algorithm.

ANN DEVELOPMENT The data set for training the networks consisted of a total of 10,000 input-output exemplars. Each exemplar recorded the TGP (as expressed by the 9 temperature readings of the sensors) and the corresponding dowel bar bending moment in N.m. The sensor reading were recorded at a frequency of 20 minutes, which means that the 10,000-point data set corresponded to temperature and bending moment readings recorded over a period of about 139 days. For testing the network, a new data set, corresponding to data recorded during the 15 days following the end of the training set, was extracted. This test set thus consisted of a total of 1080 data points, which were used in testing all ANNs developed, as will be described later in this paper. As was previously mentioned, in this study, we experimented with two different dynamic ANN topologies (namely: (1) TLNN; and (2) Elman and Jordan networks) to predict dowel bending moment from the temperature gradient profile. Our decision to use dynamic ANNs as opposed to static networks was motivated by the fact that our data was indeed in the form of a time series, and from our belief that the TGP has a direct impact on the dowel bending moment. Time Lagged Neural Networks For the TLNN, the study used the TDNN architecture, whose memory structures are of the tap delay line type. A focused topology where the memory structures are only provided at the input layer was used to allow for using the standard back propagation algorithm in training the network (the standard back propagation is much more stable than the more complex BPTT algorithm required for topologies other than the focused topology). The tap delay was set at 10, meaning that the network would use the current temperature gradient, along with the temperature gradient for the previous 10 data points (i.e. last 200 minutes) in predicting the dowel moment. One hidden layer, consisting of 14 neurons, was used. The activation function for the hidden layer neurons was a Tanh function. The TDNN will be referred to as ANN1 in this paper. Elman and Jordan Networks Three different Elman and Jordan network topologies were tried in this study. The first topology was a variant of the Elman network, where the input was copied to the context PE layer (instead of feeding the hidden layer output), providing for an integrated past of the input (memory traces). This Elman-variant network will be referred to as ANN2 in this paper. The second topology was a traditional Elman network, where the hidden layer output was fed back to the context PE layer (ANN3). Finally, the third topology was a traditional Jordan network, connecting the network output to the context layer (ANN4). Figure 9 illustrates the differences among the three network topologies tried in this study.




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For all three models, one hidden layer was used consisting of “Tanh-type” neurons. The number of neurons in the hidden layer was 85 for ANN2, and 40 for ANN3 and ANN4. The use of the relatively large number of neurons in the hidden layer was possible since an adequate number of training exemplars was available (10,000 exemplars). RESULTS The development and the training of the ANNs were conducted using the NeuroDimensions software developed by NeuroDimension, Inc (20). The training data consisting of 10,000 exemplars was divided into two groups: the training data set (8500 exemplars or 85%), and the cross-validation data set (1500 exemplars or 15%). The cross-validation set was used to test the ability of a network to generalize, while the network was still being trained. This helps safeguard against the possibility of the network “memorizing” the training pattern (over-fitting), which could lead to deterioration in the ability of the network to generalize. Training was continued until there was no further improvement in the mean square error for the crossvalidation data set during 100 epochs, or until the number of epochs reached 1000. The following sections will briefly summarize the results obtained. Results for Focused TDNN During training, the TDNN (ANN1) had a Mean Square Error (MSE) of 0.0138 on the cross validation data set. The network performance on the test set (i.e. the new 1080 data points) was even slightly better, with a Mean Square Error of 0.0130. Figure 10 shows a plot of the bending moment predicted by ANN1 versus the actual moment as recorded by the sensors. For clarity of presentation, the duration of each plot is set at 5 days (i.e. 360 data points). That is to say, the first plot is for the first 5 days following the end point of the training data set, the second plot is for the following 5 days (i.e. day 5 – day 10), and so on. As can be seen, the performance of the model appears quite good, with the predicted values very close to the recorded values, and exhibiting the same general trend. For this case, the average absolute difference between the predicted and recorded bending moment value was 14.21 N.m. Given that the average absolute value of the bending moment for the test set was 92.79N.m, the average absolute error represents only a value of 15.32% of the average absolute bending moment value. Results for an Elman Network For the Elman/Jordan networks, the Elman-variant network (ANN2) gave the best performance. For ANN2, the MSE on the test set was only 0.010. This compares to a value of 0.026 for ANN3, and a value of 0.024 for ANN4. Figure 11 shows a plot of the predicted versus recorded bending moment for ANN2. Once again, the performance of the ANN appears quite good, with the predicted values very close to the recorded values. The average absolute difference between the predicted and recorded bending moment value in this case was 12.69 N.m, which represents a value of 13.68% of the average absolute bending moment value. Comparing the TDNN to the Elman-variant network, the Elman-variant network appears to slightly outperform the TDNN.




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Tuning the Network Parameters Efforts were made to tune the network parameters. For the TDNN, we experimented with changing the tap delay value. Specifically, we experimented with values of 5, 10 and 15. We then experimented with changing the number of neurons in the hidden layer. We tried 15 neurons, 40 neurons and 85 neurons. However, the original configuration of a tap delay value of 10, and 14 neurons in the hidden layer yielded the best results. Similar tuning efforts were made to the Elman-variant network (ANN2). First, we experimented with changing the feedback parameter. Values of 0.70, 0.80, and 0.85 were tried. The number of neurons in the hidden layer was also changed to 40 neurons and to 14 neurons. The networj with a feedback parameter of 0.80 and 85 neurons in the hidden layer yielded the best performance.

CONCLUSIONS In this study, dynamic ANNs were formulated for predicting the dowel bending moment as a function of the temperature gradient profile. Several topologies were examined, and their performance was compared on a test set. Among the main conclusions of the study are: (1) Dynamic ANN are capable of capturing the relationship between the temperature gradient profile, and the dowel bending moment (2) While the performance of both the TDNN and Elman/Jordan type networks was quite good, the Elman-variant network appears to slightly outperform the TDNN. (3) For the different Elman/Jordan network topologies examined in this study, the Elmanvariant network, which fed the input to the context PE layer (Figure 9), appears to be the most appropriate topology for the problem at hand. (4) For dynamic ANNs, a number of design parameters, such as the value of the tap delay for TDNNs, the value of the feedback parameter for Elman/Jordan networks, and the number of neurons in the hidden layer, could have an impact on the network performance. Given this, it is recommended that an analysis of the sensitivity of the network performance to the values of these parameters be conducted as a part of any ANN development effort, in an attempt to improve the network performance.




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References 1. Lee, B. J. and H. Lee. (2001). Development of Efficient Tile-Based Neural Network Algorithms for Pavement Crack Analysis. A paper presented at the 80th Annual TRB Meeting, Washington, D.C. 2. Shekharan, A. R. (1999). Assessment of Relative Contribution of Input Variables on Pavement Performance Prediction by Artificial Neural Networks. A paper presented at the 78th Annual TRB Meeting, Washington, D.C. 3. Ceylan, H., E. Tutumluer, and E. J. Barenberg. (1999). Artificial Neural Network Analysis of Concrete Airfield Pavements Serving the Boeing B-777 Aircraft. A paper presented at the 78th Annual TRB Meeting, Washington, D.C. 4. Abdekrahim, A.M. and K. P. George. (2000). Artificial Neural Network for Enhancing Pavement Maintenance Strategy Selection. A paper presented at the 79th Annual TRB Meeting, Washington, D.C. 5. Martinelli, D. R. and S. N. Shoukry. (2000). Performance Evaluation of Neural Networks in Concrete Condition Assessment. In Transportation Research Record 1739, TRB, National Research Council, Washington, D.C. 6. Lou, Z., J. John Lu, M. Gunaratne, and B. Dietrich. (1999). Forecasting of Pavement Crack Condition Using A Neural Network Model. A paper presented at the 78th Annual TRB Meeting, Washington, D.C. 7. Westergaard, H.M. (1927). Analysis of Stresses in Concrete pavements Due to Variations of Temperature. Proceedings of the 6th Annual Meeting of the highway Research Board, pp. 201-215. 8. ERES Consultants. (2000). Evaluation of Pennsylvania I-80 JPCP Performance in PennDoT District 1-0 and 3-0. (Draft Final Report). Northeast Chapter, American Concrete Pavement Association, Richmond, VA 9. Thomlinson, J. (1940). Temperature Variations and Consequent Product by Daily and Seasonal Temperature Cycles in Concrete Slabs. Concrete Constr. Engrg, 36 (6), 298307, and (7) 352-360. 10. Teller, L.W., E.C. Sutherland (1935). The Structural Design of Concrete Pavements, Part 2: Observed Effects of variations in temperature and Moisture on the Size, Shape and Stress resistance of Concrete Pavement Slabs. Public Roads 16( 9), pp. 169-197. 11. Shoukry, S.N. (2000). Backcalculation of Thermally Deformed Concrete Pavements. Transp. Res. Rec. 1716, pp. 64-72. 12. Shoukry, S.N. (2002). West Virginia Instrumented Concrete Pavement: Curing and Temperature Induced Strains during the First 90 Days. Presented at the Data Analysis Working Group, 81st Annual Transportation Research Board Meeting, Washington, D.C., January 2002. 13. Sargand S.M. (2000). Performance of Dowel Bars and Rigid Pavement, Draft Final Report, Ohio University, Ohio Research Institute for Transportation and The Environment, Athens, Ohio. 14. William, G.W., and S.N. Shoukry (2001). 3D Finite Element analysis of Temperature Induced Stresses in Dowel Jointed Concrete Pavements. Int’l Jnl Geomechanics, 1(3), pp. 291-307.




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15. Sixbey, D., M. Swanland, N. Gagarin, and J.R. Mekemson (2001). “Measurement and Analysis of Slab Curvature in JPC Pavements.” Proceedings of 7th International Conference of Concrete Pavements, Volume 1, Orlando, Florida, pp. 81-96. 16. Rosenbalt, F. (1961). Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms. Spartan Press, Washington. 17. Minsky, M and S. Pappert. (1969). Perceptrons: An Introduction to Computational Geometry. MIT Press, Cambridge, MA. 18. Rumelhart, D. E. and J. J. McLelland. (1986). Parallel Distributed Processing. MIT Press, Cambridge, MA. 19. Principe, J.C., N. W. Euliano, and W. C. Lefebvre. (2000). Neural and Adaptive Systems: Fundamentals through Simulations. John Wiley & Sons, Inc. 20. NeuroDimensions, Inc. (2001). NeuroSolutions On-line Manual, Version 4.1. Gainesville, Florida.




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LIST OF FIGURES Figure 1.

3DFE Modeling of Dowel Bar Bending Due to Curling of 10 in. thick

Figure 2.

Robert Byrd's Instrumented Highway Section (Route 33), Elkins, WV.

Figure 3.

Time History of Temperature Profile Through Slab thickness

Figure 4.

Time History of The Difference Between Slab Top and Bottom Temperatures

Figure 5.

Instrumented Dowel for Continuous Monitoring of Bending

Figure 6

Time History of Bending Moment Induced in the Shoulder-side Dowel Bar.

Figure 7.

ANN Training as Function Approximation (19)

Figure 8.

The Elman and Jordan Neural Networks

Figure 9.

The Different Elman/Jordan Network Topologies

Figure 10.

Predicted versus Recorded Bending Moment for ANN1

Figure 11.





a. Slap top temperature is 10 ºC less than on Slab Bottom.

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b. Slap top temperature is 10 ºC more than on Slab Bottom.

Figure 1 3DFE Modeling of Dowel Bar Bending Due to Curling of 10 in. thick, (Shown is a Section through the Sixth Dowel from the Shoulder Side).




(a) Typical Slab Instrumentation.

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(b) Pavement after Full Construction.

Figure 2 Robert Byrd's Instrumented Highway Section (Route 33), Elkins, WV.




14

50

14 10

40

6 Temperature, ºC

30 2 20

1500

1600

10

0

10 0

500

1000

1500 Time, hr

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Figure 3 Time History of Temperature Profile Through Slab thickness




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12 (Ttop - Tbot ), ºC

8 4 0 -4 -8 0

50

100

150

200

250

Time, days

Figure 4 Time History of The Difference Between Slab Top and Bottom Temperatures.




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(a) Instrumented Dowel

(b) Laboratory Clibration

(c) Field Mounting

Figure 5 Instrumented Dowel for Continuous Monitoring of Bending Moment.



Dowel Bending Moment, lb.in


(a) Right Shoulder

200

100

0

-100

Dowel Bending Moment,

17

0

500

1000 Time, hr

1500

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(b) 20 0 100

0

-100 1500

1600

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1800

1900

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Time, hr

Temperature, ºC

45

(c)

30 15 0 0

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1000 Time, hr

Figure 6 Time History of Bending Moment Induced in the Shoulder-side Dowel Bar.



Sadek, Shoukry and Riad Figure 7.

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ANN Training as Function Approximation (19)

x

Unknown Function f(.)

f ^ (x, w)


d

y

-

+

ε



19

The Elman and Jordan Neural Networks

Jordan Network

Elman Network

Output

Output

Hidden

Hidden

Context


Input

Context

Input



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The Different Elman/Jordan Network Topologies

Context PE’s

Elman-variant Network (ANN2)

Input Layer

Hidden Layer

Output Layer

Context PE’s

Elman Network (ANN3)

Input Layer

Hidden Layer

Output Layer

Jordan Network (ANN4)

Input Layer


Hidden Layer

Output Layer



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Predicted versus Recorded Bending Moment for Days 0 - 5 Bending Moment (N.m)

200 150 100 50

Recorded Predicted

0 -50 1

31 61 91 121 151 181 211 241 271 301 331

-100 -150 Data point

Bending Moment (N.m)

Predicted versus Recorded Bending Moment for Days 5 - 10 200 150 100 50 0 -50 1 -100 -150

Recorded Predicted 31

61

91 121 151 181 211 241 271 301 331

Data Point


Predicted versus Recorded Bending Moment for Days 10 - 15 250 200 150 100 50 0 -50 1 -100 -150

Recorded Predicted

33

65

97 129 161 193 225 257 289 321 353

Data Point




Figure 11.

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Predicted versus Recorded Bending Moment for ANN2 Predicted versus Recorded Bending Moment for Day 0 - 5


200 150 100 50

Recorded Predicted

0 -50 1

31

61

91 121 151 181 211 241 271 301 331

-100 -150 Data Point

Predicted versus Recorded Bending Moment for Day 5 - 10


200 150 100 50 0 -50 1

31

61

91 121 151 181 211 241 271 301 331

Recorded Predicted

-100 -150 Data Point


Predicted versus Recorded Bending Moment for Day 10 - 15

250 200 150 100 50 0 -50 1 -100 -150

Recorded Predicted

33

65

97 129 161 193 225 257 289 321 353

Data Point



Dynamic Artificial Neural Networks for Dowel Bending ...

Dynamic Artificial Neural Networks for Dowel Bending ...

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COMMERCIAL HARDWARE FOR ARTIFICIAL NEURAL NETWORKS ...

Artificial neural networks for automotive air ...

Determining Optimum Structure for Artificial Neural Networks

Artificial Neural Networks for Satellite Image

Artificial Neural Networks For Spatial Perception

Applying Artificial Neural Networks for Face Recognition

BrainNetCNN: Artificial Convolutional Neural Networks for ... - SFU

Dynamic Artificial Neural Networks with Affective Systems - PLOS

Artificial Neural Networks for Beginners - arXiv