Application of ANN in Pavement Engineering: State-of-Art

There has been much discussion about the impact and future of artificial intelligence (AI) in our lives and future generations. Many experts even believe that AI will “rule” the world. Artificial Neural Networks (ANN) have provided a convenient and often extremely accurate solution to problems within all fields, and can be seen as advanced general-purpose regression models that try to mimic the behavior of the human brain. The adoption and use of ANN-based methods in the Mechanistic-Empirical Pavement Design Guide is a clear sign of the successful use of neural nets in geomechanical and pavement systems. This work aims to provide an extensive and detailed state-of-the-art of the application of ANN models to pavement management, materials and design problems. Unlike former review articles published before 2014, this work is more descriptive and makes the review much more appealing to the reader by highlighting numerically and/or graphically the effectiveness and possible drawbacks of each ANN application.


Artificial Intelligence and Machine Learning
There has been much discussion about the impact and future of artificial intelligence (AI) in our lives and future generations, and it has even been said by many experts that evolve in order to adapt to the surrounding environment, ANNs need to go through an adaptation/learning process in order to perform well. ANNs can be seen as advanced general-purpose regression models that try to mimic the behavior of the human brain, although at present no ANN is anywhere near to recreating the complexity of the brain.
However, the progress that has been made since their inception is remarkable, and it is certain that the development and applications of these algorithms will keep growing in the future (Flood 2008, Haykin 2009).

Application of ANN in Civil Engineering
Although genetic algorithms (GA) have often been employed successfully (e.g., Santos and Ferreira 2012, Jorge andFerreira 2012, Santos et al. 2017, to cite some recent work from the second author), ES and ANN have been the most commonly used AI techniques in Civil Engineering since the latter's inception in the mid-1980s (Mosa et al. 2013). ANN have provided a convenient and often highly accurate solution to problems within all branches, appearing from the statistics on publications to be one of the great successes of computing (Flood 2008). The first journal article on civil engineering applications of neural networks was published by Adeli and Yeh (1989). Since then, many other applications of ANN within all fields of Civil Engineering have arisen with increased complexity and sophistication (Adeli 2001). Because of their much faster response in comparison to FEA, they are often used in approximation for structural analysis (in particular, parametric analysis can then be performed without spending so much time), as well as in the active control of structures (Sheidaii and Bahraminejad 2012). Areas like (i) buckling and bearing capacity prediction Class I Class III

Aim
Due to (i) the extent of ANN-based applications in pavement engineering since the 1990´s, and (ii) the rising potential of neural nets to the performance of more accurate and efficient engineering, this work aims to provide an extensive and detailed state-of-the-art application of ANN models in the design and management of pavements. Unlike previous review articles published on these topics before 2014 (Dougherty 1995, Flintsch et al. 2004, Kim et al. 2009, it is worth noting that the present work is far more descriptive and makes the review much more appealing to the reader by highlighting numerically and/or graphically the effectiveness and possible drawbacks of each ANN application.
After briefly addressing the ANN features and fundamentals in the next section, the applications of neural nets to several types of pavement problems are described in detail in section 3.

Brief Overview of ANN Features and Fundamentals
This section addresses the main neural network features and gives a short overview about the main concepts inherent to the most typical ANN models employed in pavement engineering so far. Further details about virtually any topic regarding ANN can be found in well-known books like Haykin (2009) or Du and Swamy (2014).
The general ANN structure can be seen as several partially or fully connected processing units (neurons), which are disposed in several vertical layers (the input layer, hidden layers if there are some, and the output layer), as illustrated in Fig. 3. Associated to each neuron is a linear or nonlinear transfer (also called activation), function, which receives an input and transmits an output -a typical neuron's model is described in 2.1. Each connection (link between two nodes in the network), is associated to a synaptic weight, which is a typical example of a network unknown to be determined during the network design process. The ANN's computing power, making them suitable for efficiently solving complex (small to large-scale), intractable problems, can be attributed to their (i) massive parallel distributed structure and (ii) ability to learn and generalize, i.e, produce reasonably accurate outputs for inputs not used during the training phase. Besides, neural networks offer the following useful features: (i) Nonlinearity: guaranteed when at least one neuron's transfer function is nonlinear.
(ii) Input-output mapping: in the context of nonlinear vector mapping problems comprising a fixed set of independent variables, ANN-based solutions are frequently more accurate than the ones provided by traditional approaches (e.g., multi-variate nonlinear regression), despite the fact they do not require a good knowledge of the function shape being modeled (Flood 2008).
(iii) Adaptivity: a neural network trained to operate in a specific environment can be easily retrained to deal with minor changes in that environment (e.g., when operating in a nonstationary environment).
The way in which the neurons of a neural net are structured and linked define what is known as the network architecture. In general, one may identify three fundamentally different classes of network architectures: (i) Single-Layer Feedforward Network, (ii) Multi-Layer Feedforward Network, and (iii) Recurrent Networks (RNN) (Haykin 2009). In sub-section 2.2, the multi-layer perceptron (MLP) is briefly addressed since it is the most commonly used network type in pavement engineering applications.

Model of a Neuron
Each processing unit (sometimes called computation node) of an ANN is called a neuron, and it plays a crucial role in the network's behavior. There are three basic elements in a typical model of a neuron, as depicted in Fig. 4: (i) connecting links (also called synapses) between each "input" signal (xj , j=1,...,J) and the k th neuron, which are characterized by their synaptic weights (wjk R  ), (ii) a summing junction (sk = xj wjk) -Einstein summation convention employed, to add up the weighted input signals that converge to the neuron, and (iii) an activation (or transfer) function φk, which receives sk plus neuron's bias (bk R  ) as inputalso known as the induced local field, and provides neuron's output yk. In ANN design, the activation functions are user-defined (e.g., logistic, linear). x 1 w 1k This is a feedforward ANN, i.e. the signal flow through the network progresses in a forward direction from left to right, and on a layer-by-layer basis, and exhibits at least two neuron-based layers and the input node layer. Each layer of neurons that is not the output layer is called a "hidden layer" and the corresponding units are called "hidden neurons". By adding one or more hidden layers, the network is enabled to extract higher-order statistics from its input (Haykin 2009). Fig. 3 represents a 3-layer feedforward network, also referred to as 3-4-2 (3 input nodes, 4 hidden neurons in the single hidden layer, and 2 output neurons).
As can be seen, each node in each layer links to every node in the next layer (typically called a fully-connected network), i.e. the output signals of the 2 nd (hidden) layer will serve as input signals of the 3 rd (output) layerunless stated otherwise (e.g., PC -partially connected), all MLP networks mentioned in this paper are fully-connected. Nodes in each layer do not connect to each other and no connections across layers (between the input and output layers, in this case) are allowed. The synaptic weights and bias mentioned in 2.1 are network unknowns to be computed through the learning process, which is addressed next.

Knowledge and Learning
In ANN, as in any other machine learning technique, a good solution depends on a good representation of knowledge (Woods 1986), which makes the development of such networks a real design challenge. For a specified network architecture, that knowledge representation is defined by the values taken on by the free parameters (or unknowns) of the network (e.g., synaptic weights and bias), which are determined by a major task for any ANN, called Learning. This stage typically consists of two phases: (i) training and (ii) validation. From the obtained knowledge, examples (also known as "data points" or "training set") are selected to train the neural network. These examples are said to be "labeled" or "unlabeled", depending on whether they represent an input paired with the target output (desired "response") or just the input itselfin most cases addressed so far in pavement engineering, the performed learning is called "supervised", since all the examples considered are "labeled". One of the convergence criterion most often employed in the design of ANNs is called "early stopping", and it is a cross-validation of the network performance during training. This means, as Fig. 5   Among the most popular training techniques that can be employed to get the neural network free parameters (or unknowns), namely the Back-Propagation (BP) and the Levenberg-Marquard (LM) algorithms, the most effective and robust is the latter (Wilamowski and Yu 2010a, b). More recently, a new algorithm called Extreme Learning Machine (ELM) was proposed by Huang et al. (2006a, b) and since its inception several variants / improvements of it have been proposed in the literature (e.g., Liang et al. 2006, Huang and Chen 2007, Miche et al. 2010, Huang et al. 2011). In the authors' opinion, ELM is quite easy to implement and is the most powerful of all training methods developed so far.
However, it hasn´t been applied in pavement engineering because it might not be implemented in commercial machine learning codes yet.

The Universal Approximation Theorem
For a nonlinear input-output mapping, this theorem states (Haykin 2009) that a single hidden layer MLP, with (i) any bounded, monotone-increasing and continuous activation function for the hidden neurons, and (ii) an identity (linear) transfer function for the output neurons, is sufficient to compute an arbitrarily good approximation of any continuous function in a general n-dimensional spacethe absolute difference between any estimated and target outputs can be less than any ε > 0, for all input space values. However, it is worth recalling that this theorem does not guarantee great network behavior for learning time and/or generalization.

Data Pre-Processing and Tuning of Network Layout
In order to get the most out of the neural network abilities, it is highly recommended that the data is correctly selected and pre-processed before learning starts. To that end, there are several approaches worth considering, such as (i) input variable selection algorithms (e.g., May et al. 2011), (ii) dimensional analysis (e.g., Bhaskar and Nigam 1990), (iii) dimensionality reduction techniques (e.g., principal component analysis) (e.g., May et al. 2011), and (iv) normalization (e.g., Flood andKartam 1994a, Azoff 1994).
A rule of thumb for obtaining good generalization in systems trained by examples is that one should use the smallest system that will fit the data (Reed 1993, May et al. 2011.
Several guidelinesmostly (if not all) obtained from trial and error, (i) for choosing an adequate initial number of hidden neurons/layers and also (ii) for network pruning (size reductionnodes and/or connections), are available from many sources (e.g., Mozer and Smolensky 1989, Weigend et al. 1991, Reed 1993, Basheer and Hajmeer 2000, Rafiq et al. 2001, Olden and Jackson 2002.

Roughness
A pavement profile (also called roughness) is one of the most effective vehicle environmental conditions that influences ride, handling, fatigue, fuel consumption, tire wear, maintenance costs and vehicle delay costs.
Roberts and Attoh-Okine (1998) compares the use of two ANN models to predict roughness based on pavement condition characteristics and traffic. The study uses 105 data points characterized by 11 variables of 5 types (rutting, fatigue cracking, transverse cracking, block cracking, equivalent axle loads and the international roughness index (IRI)), with IRI being the target variable of the problem and the others the input counterpart.
From that dataset, 75 examples were taken for training purposes and 30 for validation. One of the proposed neural net is a BP-based 10-5-1 MLP, and the comparison model is called quadratic function ANN. It is a feedforward net exhibiting a generalized adaptive architecture, which uses a combination of supervised and self-organized (unsupervised) learning. This type of network uses an evolutionary mechanism to fit the problem at hand and does not require the modeler to specify the number of layers / nodes. It was shown that the latter model (R 2 = 0.74) outperforms the traditional MLP network (R 2 = 0.57).
Yildirim and Uzmay (2001)  An ANN-based prediction of road profiles has been demonstrated by Ngwangwa et. al (2014), who developed a LM-based 3-50-50-2 MLP network trained with 3964 data points obtained numerically. Validation was carried out using measured data. The results show very good correlations, even over discrete obstacles. Ziari et al (2016) proposed an ANN to predict IRI values in the short-and long-term for flexible pavements. Sensitivity analysis using several LM-based MLP networks was performed, parameterizing the number of hidden layers (1 to 3) and nodes (3 to 100) in order to find an optimal model. From the databank used in learning (205 data points), 154 samples were used in training, 41 in validation and 10 in testing. It was concluded that ANN models predict the future of pavement condition with satisfactory accuracy in the short-and long-term. Whereas (i) the best performance regarding the first category (short term) was obtained for the topology 9-80-50-30-1, (ii) structure 9-3-1 yielded the best performance in the second category (short term), and (iii) 9-8-1 proved to be the best layout in the third category (long term). Even so, layouts like 9-5-1, 9-7-1, 9-20-1 and 9-50-1 exhibited MAPE < 10% and R 2 > 0.9 for the testing set.

Skid Resistance
It is well known that weather and traffic influence the degradation of skid resistance between the tire and pavement surface over time.
Owusu-Ababio (1995) implemented an ANN to predict skid resistance of flexible pavements in order to assess future rehabilitation needs. Only original bituminous concrete pavements with no overlays were considered. The data used were 45 observations for training and 15 for validation, featuring (i) skid number (output or target variable), (ii) pavement surface age, (iii) pavement regional location, (iv) accumulated AADT (Annual Average Daily Traffic) and (v) posted speed limit. A partially connected 4-3-2-1 MLP was employed, as shown in Fig. 6. The software used to design the ANN (Autonet) uses adaptive modeling proceduresthe basic approach is that (i) exactly two nodes must connect to any neuron in the next layer and (ii) the number of layers and neurons per layer are limited once the network performance gets worse. It was observed that the ANN validation error is much lower than that obtained from the linear regression approach. Bosurgi and Trifirò (2005) developed a neural net-based "sideway force coefficient" prediction model to be applied on a motorway. The database included 713 samples, from which 463 were selected at random for training and the remainder for validation. A LM-based 2-3-1 MLP was adopted. The results confirmed that the neural network had interpreted the phenomenon well, since an error inferior to 7% was observed in 91% of the cases in the training phase and 86% in the validation phase.

Cracking
Cracking is one of the primary forms of distress in hot-mixed asphalt pavements. In recent years, Paris' law, which is based on linear elastic fracture mechanics, has been adopted to analyze pavement cracking problems. However, one of the drawbacks of this model regards the quick and accurate computation of the stress intensity factors (SIF), a parameter that amplifies the magnitude of applied stress, at crack tips. Finite element analysis (FEA) is a powerful tool for that purpose, but the 3D pavement behavior can only be accurately predicted using 3D FEA, and unfortunately that computation is still too heavy (slow) when using today's available resources in practical applications. Kaseko (1993) proposed an ANN for automatic detection, classification and quantification of pavement surface cracking, based on processing pavement images.
Pavement cracks can accurately be classified by type (e.g., transverse, longitudinal, alligator and block), severity and extent. For that purpose, binary images are divided into tiles and each tile is analyzed to determine the existence and orientation of any crack in it. A BP-based 5-5-5 MLP was used for this task. Twenty images were selected for training and validation purposes. Overall, the neural net classified more than 96% of the tiles in the training images and 93% in the validation counterpart.
Owusu-Ababio (1998) where Hv is the vertical histogram and Nc the number of columns of the "tiled" image, (ii) horizontal proximity (Ph), defined as where Hh is the horizontal histogram and Nr the number of rows of the "tiled" image, and assessed (2-3 hidden layers, 4-7 hidden nodes) and models corresponding to the best performance were selected. Fig. 10 shows the evolution of performance measures as a function of the ANN topology used for the raveling progression models. The best ANNs exhibit the following layouts: (i) 26-7-7-7-1 (cracking), (ii) 26-5-5-1 (raveling), (iii) 29-7-7-7-1 (roughness), (iv) 31-6-6-1 (rut-depth). were investigated for every neural net model and the results showed that 7-60-60-1 (fatigue cracking) and 9-60-60-1 (reflective cracking) layouts yield the best performance. Besides the fact that ANN models are quite efficient in getting results once designed (> 30000 cases in less than a second), it also was shown that their performance clearly surpasses the nonlinear regression counterpart.
Gajewski and Sadowski (2014) proposed a FEA-ANN system, based on BP-based 4-7-2 MLP network and 4-5-2 RBFNN for the prediction of crack sensitivity in a subgrade layer.
Input variables included asphalt pavement layer parameters and different load modes, and the expected output response would predict crack occurrence. FEA results were used as learning data (quantity not disclosed). The MLP performed far better than the RBFNN in the classification task, having yielded accuracies of (i) 94% vs. 65% in learning, (ii) 98% vs. 62% in validation and (iii) 92% vs. 77% in testing, respectively.    networks were assessed parametrically in order to find the optimal layout, which was 8-8-8-1.
The proposed ANN was able to successfully predict the measured joint faulting with R 2 =0.94 for the testing set. However, there are significant relative errors concerning small value faulting, especially for the testing set.

Present Serviceability Index (PSI) / Ratio (PSR)
Prediction modelling of pavement deterioration (a stochastic and nonlinear phenomenon) is crucial for an effective PMS, where the goal is to find the appropriate period and method of rehabilitation. Banan and Hjelmstad (1996)

Condition Rating
One of the important activities of highway engineers is the determination of pavement condition ratings (PCR), i.e. the assignment of relative weights to various levels of pavement distresses in order to obtain a combined score that indicates the current condition of a roadway section.
According to Pant et al. (1993), no specific guidelines were available for condition showed that a larger discrepancy between the predicted and actual outputs existed when the UCCIs were very large or very small, which is believed to have been caused by small sample sizes within these ranges. Eldin and Senouci (1995a)  The results showed that the ANN (i) was able to correctly predict condition ratings even when designed for input data containing high levels of noise, and (ii) outperformed the ODT's prediction model for subjective ratings. Pavement performance (or deterioration) assessment, a key vector of PMS, is usually undertaken through prediction of roughness progression. Eldin and Senouci (1995b) proposed an ANN based on the condition rating scheme

Maintenance
Due to time, budget and other resource constraints, it is not always possible for a highway agency to attend all road sections requiring maintenance within a given period, which calls for a scheme to rank road sections for maintenance treatment according to priority. Traditionally, ranking of highway sections requiring maintenance is based on experience of qualified personnel. Mathematical decision-making criteria have been proposed through the so-called "aggregate condition index", which has shown several drawbacks (Fwa and Chan 1993).
In order to overcome the aforementioned limitations, Fwa and Chan (1993) developed BP-based 6-1-1 MLP neural nets based on 428 (30% -training, 70% -validation), 1272 (76% -training, 24% -validation), 4396 (93% -training, 7% -validation) and 12800 data points (98% -training, 2% -validation). It was concluded that all ANNs were able to predict priority ratings within an average absolute error of about 5%. It was shown that if noise as high as 50% of the maximum rating score was introduced in the data, the error would rise to about 14%.
Hajek and Hurdal (1993) compared an ANN to an existing knowledge-based expert system called ROSE, designed to determine the need for a specific asphalt concrete (AC) pavement maintenance treatment (routing and sealing). A random training data set of 148 pavement sections was used in this study, whereas validation was carried out by means of a random set of 20 instances. The developed ANN is a BP-based 40-x-1 MLP and the obtained results were considered to be reasonably good since the final number of hidden neurons (not disclosed in the paper) was automatically computed by the software used in order to have a maximum tolerance of 10% when comparing ANN and target outputs.

Layer Moduli / Thickness, Poisson's Ratio
Backcalculation is an inverse methodology to determine in situ materials stiffness of pavement layer by matching the measured and theoretical deflection with iteration and optimization schemes. One of the drawbacks, besides time, is that minor deviations between measured and computed deflections usually result in significantly different moduli. Khazanovich And Roesler (1997) implemented an ANN to backcalculate the layer moduli of a three-layer system for a range of pavement layer thicknesses. The necessary data (25000 examples) was obtained by a computer program. Three independent ANN were trained to find (i) modulus of elasticity of the upper constructed layer (E1), (ii) modulus of elasticity of the lower layer (E2), and (iii) coefficient of subgrade reaction (k).
Whereas (i) the first ANN calculates the pavement deflection profile for a range of pavement layer parameters, in order to reduce the computational time in forward calculations using the aforementioned program, (ii) the second and third ANNs provide E2 / k and E1 / E2 outputs, making use of the estimated E2 / k obtained through the second ANN. All networks were based on an adaptive interpolation methodology with fuzzy subdomains, and they were trained until the relative error was smaller than 1%. Their layout is similar to that of a hierarchical adaptive random partitioning (HARP) network.
When an impact is made on a pavement surface of a semi-infinite half-space, surface waves are generated and travel along the surface of the half-space. These surface waves penetrate different depths depending on their wavelengths. Kim and Kim (1998) trained several MLP neural nets (learning algorithm not disclosed) to map phase velocities with the corresponding layer moduli (no. of layer moduli are the number of output nodes). Learning data was generated numerically and consisted of 600, 1000 and 2000 data points (training -50%, validation -50%) for two, three and four-layered pavement systems, respectively. In addition to thickness-related variables (one, two or three variables for two-, three-or four-layered systems, respectively), 19 phase velocity variables were considered as input variables. The MLP network layouts 20-28-2, 21-34-3 and 22-45-4, respectively regarding two-, three-and four-layered pavements, were employed (learning algorithm not disclosed). Very good results were obtained, namely average and maximum errors lower than 2.5% and 8.7%, respectively. Ceylan et al. (2007) validated ANN models to predict layer moduli as a function of FWD deflections and layer thicknesses. A total of 24093 runs in a FE program were carried out for data generation (1000 points used for validation and 23094 for training).
The BP-based 6-60-60-2 MLP was chosen as the best model for elastic moduli prediction, and the BP-based 12-60-60-1 MLP was adopted to estimate the K-parameter from the K-Θ granular base relationship, having yielded an average absolute error of 3.4%. Sharma and Das (2008) proposed several ANN models to backcalculate layer moduli from normal and noisy deflection basins and layer thicknesses. After trial-and-error of several BP-based MLP topologies (1-2 hidden layers, 7-20 hidden nodes per layer), it was concluded that one hidden layer and 10-15 neurons yields the best results. A total of 6000 sets of deflection basin data are used, 5800 of those employed in network training. The performance of the ANN was found to be satisfactory in terms of (i) computation time and (ii) accuracy. Gopalakrishnan (2008) developed an ANN to backcalculate airport flexible pavement moduli based on heavy weight deflectometer (HWD) test data. Three thousand, seven hundred and fifty data vectors were used in training and 1250 in validation. Separate ANN models were used for each output variable and parametric analysis was carried out to select the best architectures. Concerning AC and subgrade moduli prediction, the BP-based 6-40-40-1 (average absolute error in validation = 8.2%) and 8-40-40-1 (average absolute error in validation = 7.6%) MLP nets produced the best results, respectively. Gopalakrishnan and Ceylan (2008) employed ANN-based structural models to accurately predict flexible airport pavement layer moduli from realistic FWD deflection basins. Data for ANN learning was numerically obtained, with 23093 points for training and 1000 for validation. Two separate models were proposed for the prediction of AC and subgrade Young modulus, as a function of six pavement surface deflections and two layer thicknesses (8 input variables). The developed BP-based 8-60-60-1 MLP models exhibited average absolute errors smaller than 1.5% for the validation subset, as shown in Fig. 13. Bayrak and Ceylan (2008) proposed two ANNs to backcalculate rigid pavement parameters using FWD data. To train those models, 39026 and 49539 FEA-based samples were used in the training of elastic modulus and coefficient of subgrade reaction, respectively, whereas 2000 different examples were taken for validation of each ANN. The designed models were BP-based 8-60-60-1 and 7-60-60-1 MLP nets, respectively, both associated with average absolute errors smaller than 0.3%. Park et al. (2009) proposed several neural networks to predict RM of subgrade and subbase pavement materials from several basic soil properties. For subgrade soils, 236 and 36 data points were employed for training and validation, respectively, with 164 and 26 being the size of the subbase soil-related subsets. The best performing ANN schemes were the BP-based 6-4-1 (subgrade) and 3-5-1 (subbase) MLPs, which yielded great results (e.g., R ≥ 0.975 for the best subbase material model). data points) showed that, for all models except the base thickness, at least 90% of the results had a relative error equal or smaller than 20%, which is quite satisfactory.
Xiao and Amirkhanian (2009)  , 0 Nazzal and Tatari (2013) used GA and BP-based ANNs to predict subgrade RM based on soil index properties. RM test results were collected to construct a databank. MLP and RBF nets with different numbers of hidden nodes were tested, and the selected models for the prediction of several coefficients were: 5-4-1 MLP (k1), 4-7-1 MLP (k2), 5-8-1 MLP (k3). GA were then used to analyze whether better prediction models could be devised by selecting the ANN input variables, resulting in the following optimal models: 10-10-1 MLP (k1), 9-9-1 MLP (k2), 7-6-1 MLP (k3), which outperformed the former ones and yielded great validation results (R 2 > 0.92). However, it should be borne in mind that the models that did not use GA did not employ any technique for input variable selection, which means it is not a fair comparison with the GA-based counterpart. Singh et al. (2013) developed an ANN that integrates aggregate shape parameters in the estimation of dynamic modulus. A total of 1440 dynamic moduli measured values were used in learning -1152 data points were used for training and 288 for validation. A LM-based 8-20-20-1 MLP network was designed after hidden node-based sensitivity analysis. It was shown that the inclusion of aggregate shapes enhanced the prediction capability of the model, which exhibited a mean absolute relative error of 10.2% and 17.5% for the training and validation subsets, respectively. Saltan et al. (2013) developed an ANN-based backcalculation procedure where the data used were obtained through 114 FEA, including surface deflections for long-term pavement performance (input variables) and AC elastic modulus and Poisson's ratio. In this data, 95 data points were used for training and the remainder for validation. The final design was obtained with a LM-based 7-15-3 MLP network, which yielded a mean absolute relative error less than 3.5% for any subset.
By means of an ANN model, Tarawneh and Nazzal (2014)  were generated. A BP-based 13-20-20-3 MLP network was found to be the most appropriate and proved to yield highly correlated estimations (R 2 ≥ 0.99).
In order to obtain data for this study, 5000 flexible pavement sections were analyzed using layered elastic theory (3000 in training, 500 for cross-validation and 1500 for testing).
The LM-based 7-15-4 MLP network has proven to be a highly accurate model (R 2 =0.999).

Frequency of application of each ANN feature
In this final sub-section, Tabs. 1-4 summarize the main ANN design features employed per pavement engineering problem addressed in this paper, so that the reader can decide much quicker which features to include in a neural net-based parametric analysis of similar problems. (ii) The error backpropagation has been the most employed learning algorithm in any of the three pavement engineering fields addressed, having been used in more than 55 % of the works.
(iii) The logistic hidden node transfer function is by far (90.9 %) the "winner" in pavement management problems. In the other two fields, it also takes the lead but by less than an eleven percent point difference over the hyperbolic tangent function.  (iv) For the output neurons, the logistic transfer function predominates in all fields except pavement distresses, where the linear function was employed in 63.6 % of the cases.
(v) Fig. 18 presents the distribution of the "ANN feature" in the fourth column of Tabs. 1-4 for all the references analyzed. That value represents the round of the constant amount of values (a) per input variable that needed to be considered if LD (total amount of learning data points) equaled the total number of input data combinations -"a" from a IV =LD was computed and then rounded to the closest integer, where IV is the number of input variables.    Table 4. ANN features employed in pavement materials and design problems: stress, strain, deflections, creep, material physical properties and ESAL.

Final Remarks
An extensive state-of-the-art application of ANN in pavement engineering has been presented, which has covered fields such as pavement (i) management and (ii) materials and design. This work intends to motivate and support the related expert community in the use of neural nets in problems where there is abundant data but the solving methods usually adopted are too lengthy and/or inaccurate. A graphical insight of the usage frequency of the main ANN features in pavement (i) management (distresses excluded), (ii) distresses and (iii) materials and design problems, is presented. Lastly, it should be noted that despite the great amount of applications and quite satisfactory results found in the literature, there is a lack of utilization of more advanced techniques in the design of ANNs -in most cases, the more traditional architecture (MLP) and learning algorithms (BP, LM) were employed, and not much reference was made to special trimming and data preprocessing techniques for the improvement of the network generalization ability. The authors of this paper are currently working to make a contribution to change this scenario in the near future.