Noise-tolerant inverse analysis models for nondestructive ... · Noise-tolerant inverse analysis...

Civil, Construction and Environmental EngineeringPublications Civil, Construction and Environmental Engineering

2013

Noise-tolerant inverse analysis models fornondestructive evaluation of transportationinfrastructure systems using neural networksHalil CeylanIowa State University, [email protected]

Kasthurirangan GopalakrishnanIowa State University, [email protected]

Mustafa Birkan BayrakIowa State University

See next page for additional authors

Follow this and additional works at: http://lib.dr.iastate.edu/ccee_pubs

Part of the Civil and Environmental Engineering Commons

The complete bibliographic information for this item can be found at http://lib.dr.iastate.edu/ccee_pubs/62. For information on how to cite this item, please visit http://lib.dr.iastate.edu/howtocite.html.

This Article is brought to you for free and open access by the Civil, Construction and Environmental Engineering at Digital Repository @ Iowa StateUniversity. It has been accepted for inclusion in Civil, Construction and Environmental Engineering Publications by an authorized administrator ofDigital Repository @ Iowa State University. For more information, please contact [email protected].

http://lib.dr.iastate.edu/?utm_source=lib.dr.iastate.edu%2Fccee_pubs%2F62&utm_medium=PDF&utm_campaign=PDFCoverPages

http://lib.dr.iastate.edu/?utm_source=lib.dr.iastate.edu%2Fccee_pubs%2F62&utm_medium=PDF&utm_campaign=PDFCoverPages

http://lib.dr.iastate.edu/ccee_pubs?utm_source=lib.dr.iastate.edu%2Fccee_pubs%2F62&utm_medium=PDF&utm_campaign=PDFCoverPages


http://lib.dr.iastate.edu/ccee?utm_source=lib.dr.iastate.edu%2Fccee_pubs%2F62&utm_medium=PDF&utm_campaign=PDFCoverPages


http://network.bepress.com/hgg/discipline/251?utm_source=lib.dr.iastate.edu%2Fccee_pubs%2F62&utm_medium=PDF&utm_campaign=PDFCoverPages

http://lib.dr.iastate.edu/ccee_pubs/62

http://lib.dr.iastate.edu/ccee_pubs/62

http://lib.dr.iastate.edu/howtocite.html

http://lib.dr.iastate.edu/howtocite.html

mailto:[email protected]

AuthorsHalil Ceylan, Kasthurirangan Gopalakrishnan, Mustafa Birkan Bayrak, and Alper Guclu

This article is available at Digital Repository @ Iowa State University: http://lib.dr.iastate.edu/ccee_pubs/62

http://lib.dr.iastate.edu/ccee_pubs/62?utm_source=lib.dr.iastate.edu%2Fccee_pubs%2F62&utm_medium=PDF&utm_campaign=PDFCoverPages

Reference to this paper should be made as follows: Ceylan, H., Gopalakrishnan, K., Bayrak, M. B., and Guclu, A. (2013). “Noise-

Tolerant Inverse Analysis Models for Non-Destructive Evaluation of Transportation Infrastructure Systems Using Neural

Networks,” Journal of Nondestructive Testing and Evaluation, Vol. 28, No. 3, pp. 233–251.

1

Noise-tolerant inverse analysis models for nondestructive evaluation

of transportation infrastructure systems using neural networks

Halil Ceylan, Kasthurirangan Gopalakrishnan, Mustafa Birkan Bayrak, and Alper Guclu




2

Abstract

The need to rapidly and cost-effectively evaluate the present condition of pavement infrastructure is a critical

issue concerning the deterioration of ageing transportation infrastructure all around the world. Non-destructive

test (NDT) and evaluation methods are well-suited for characterizing materials and determining structural

integrity of pavement systems. The Falling Weight Deflectometer (FWD) is a NDT equipment used to assess

the structural condition of highway and airfield pavement systems and to determine the moduli of pavement

layers which are not only good condition indicators, but are also necessary inputs for conducting mechanistic

based pavement structural analysis. This involves static or dynamic inverse analysis (referred to as

backcalculation) of FWD deflection profiles in the pavement surface under a simulated truck load. The main

objective of this study was to employ biologically inspired computational systems to develop robust pavement

layer moduli backcalculation algorithms that can tolerate noise or inaccuracies in the FWD deflection data

collected in the field. Artificial Neural Systems (ANSs), also known as Artificial Neural Networks (ANNs)

are valuable computational intelligence tools that are increasingly being used to solve resource-intensive

complex problems as an alternative to using more traditional techniques. Unlike the linear elastic layered

theory commonly used in pavement layer backcalculation, nonlinear unbound aggregate base (UAB) and

subgrade soil response models were used in an axisymmetric finite-element structural analysis program to

generate synthetic database for training and testing the ANN models. In order to develop more robust

networks that can tolerate the noisy or inaccurate pavement deflection patterns in the NDT data, several

network architectures were trained with varying levels of noise in them. Applied noise levels in deflection

basins and pavement layer thicknesses ranged from ± 2% to ± 10% to train robust ANN models that can

account for the variations in deflection measurements and pavement layer thicknesses due to poor

construction practices. The trained ANN models were capable of rapidly predicting the pavement layer

moduli and critical pavement responses (tensile strains at the bottom of the asphalt concrete layer,

compressive strains on top of the subgrade layer, and the deviator stresses on top of the subgrade layer) and

pavement surface deflections with very low average errors compared to those obtained directly from the finite

element analyses. Such use of robust ANN models developed for realistic field conditions enable pavement

engineers to easily and quickly incorporate the needed sophistication in structural analysis, such as finite

element modeling of proper characterization of unbound pavement layers, into routine practical design.

Keywords: Artificial Neural Networks; Pavement Analysis and Design; Finite Element Analysis;

Nondestructive Testing and Evaluation, Falling Weight Deflectometer, Inverse Analysis, Transportation

Infrastructure Systems.

1 Introduction

Structural evaluation of pavements provides a wealth of information concerning the expected behavior of

pavement systems (Haas et al., 1994). The falling weight deflectometer (FWD) is a non-destructive test

(NDT) device used by pavement engineers to evaluate the structural condition of highway pavements and

airport runways and to determine the moduli or stiffness of pavement layers. Over the years, the

measurements made using this type of NDT equipment have gained their own place in routine pavement

management practices in many countries (Macdonald, 2002).

During FWD testing, a dynamic load is generated by a mass free falling onto a set of rubber springs

and the device is set up to strike the pavement at a given force. Sensors placed around the plate and in a

straight line radiating from the plate record the deflections in the pavement (analogous to ripples in a pond)




3

induced by the falling weight. Thus, the FWD is an impulse-type testing device that imparts a transient load

on the pavement surface, and the duration and magnitude of the force applied is representative of the load

pulse induced by an aircraft or truck moving at moderate speeds. FWD devices are used to evaluate the load-

bearing capacity of existing pavements and provide material properties of in-situ pavement and subgrade

layers for the design of pavement rehabilitation alternatives (Macdonald, 2002).

Backcalculation is the accepted term used to identify a process whereby the elastic (Young’s) moduli

of individual pavement layers are estimated based upon measured FWD surface deflection basins. As there

are no closed-form solutions to accomplish this task, a mathematical model of the pavement system (called a

forward model) is constructed and used to compute theoretical surface deflections with assumed initial layer

moduli values at the appropriate FWD loads. Through a series of iterations, the pavement layer moduli are

changed, and the calculated deflections are then compared to the measured deflections until a match is

obtained within tolerance limits. Thus, backcalulation is an inverse analysis where the layer moduli are

estimated, the deflections calculated and compared to the measured deflections, and the moduli are modified

until calculated deflections are close to the measured deflections. Most commercial backcalculation programs

utilize an Elastic Layered Program (ELP) as the forward model to compute the surface deflections.

The nonlinear stress-sensitive response of unbound aggregate materials and fine-grained subgrade

soils has been well established (Brown and Pappin, 1981; Thompson and Elliott, 1985; Garg et al., 1998)

which the ELPs employed in asphalt pavement analysis tend to ignore. Numerous research studies have

validated that finite-element pavement structural models such as ILLI-PAVE (which can account for non-

linear geomaterial characterization) provides a realistic pavement structural response prediction for highway

and airfield pavements (Thompson and Elliot, 1985; Garg et al., 1998; Thompson, 1992).

In recent years, Artificial Neural Systems (ANSs), also known as Artificial Neural Networks (ANNs)

are increasingly being used to solve pavement engineering functional mapping problems. Although ANN

modeling was used in the past to aid in NDT-based pavement moduli backcalculation (Meier and Rix, 1995),

the structural models used to generate the ANN training database did not account for realistic stress-sensitive

geomaterial properties. Recent research studies at the Iowa State have focused on the development of ANN

based forward and backcalculation type flexible roadway pavement analysis models trained using ILLI-PAVE

solutions database to predict critical pavement responses and layer moduli, respectively. The main objective

of this study is to develop robust ANN backcalculation models that can tolerate the noisy or inaccurate

pavement deflection patterns in the NDT data acquired through FWD field tests. Neural network learning

theory draws a relationship between ‘‘learning with noise’’ and applying a regularization term in the cost

function that is minimized during the training process on clean (non-noisy) data. Application of regularizers

and other robust training techniques are aimed at improving the generalization capabilities of ANN models,

reducing overfitting (Trentin and Matassoni, 2003). This study employs a simple, straightforward technique

for training ANN models in the presence of noise as a first step towards developing robust noise-tolerant

ANN-based pavement layer moduli backcalculation models.

Solutions that are obtained in real-time are required for Pavement Management Systems (PMS)

applications due to the large volume of NDT data that has to be processed on a routine basis. The successful

application of ANNs in the back-calculation process can make the incorporation thereof possible in a PMS

due to the relatively fast execution speed associated with ANN solutions (Bredenhann and Van de Ven, 2004).




4

2 Anns Methodology

ANNs are parallel connectionist structures constructed to simulate the working network of neurons in human

brain. They attempt to achieve superior performance via dense interconnection of non-linear computational

elements operating in parallel and arranged in a pattern reminiscent of a biological neural network. The

perceptrons or processing elements and interconnections are the two primary elements which make up a

neural network. A single perceptron is mathematically represented as follows (Haykin, 1999):

n

i

jijijk bwxvy1

)(

(1)

where xi is input signal, wij is synaptic weight, bj is bias value, vj is activation potential, φ() is activation

function, yk output signal, n is the number of neurons for previous layer, and k is the index of processing

neuron.

Multilayer perceptrons (MLPs), frequently referred as multi-layer feedforward neural networks,

consist of an input layer, one or more hidden layer, and an output layer. Learning in a MLP is an

unconstrained optimization problem, which is subject to the minimization of a global error function depending

on the synaptic weights of the network. For a given training data consisting of input-output vectors, values of

synaptic weights in a MLP are iteratively updated by a learning algorithm to approximate the target behavior.

This update process is usually performed by backpropagating the error signal layer by layer and adapting

synaptic weights with respect to the magnitude of error signal.

The backpropagation training algorithm (Werbos, 1974; Rumelhart et al., 1986) for a simple three-

layer MLP structure (one input layer, one hidden layer, and one output layer) is described as follows. The

network is initially presented with an input vector (x1, x2, x3,… xN) augmented by a bias x0 = 1. The net

activations of the hidden neurons and the outputs from the hidden layer are calculated as follows:

N

i

ijijj xvnethI0

(2)

where i varies from 0 to N and j varies from 1 to L hidden neurons. The synaptic weights of the

interconnections between the inputs and the hidden neurons are represented by vji. Among the nonlinear

activation functions, the sigmoidal (logistic) function is the most usually employed in ANN application. The

presence of a nonlinear activation function, φ(), is important because, otherwise, the input-output relation of

the network could be reduced to that of a single-layer perceptron. The computation of the local gradient for

each neuron of the multilayer perceptron requires that the function φ() be continuous. In other words,

differentiability is the only requirement that an activation function would have to satisfy. The sigmoidal

function is a bound, monotonic, non-decreasing function that provides graded, nonlinear response within a

specified range, 0 to 1.The sigmoidal nonlinear activation function is given by:

)exp(1

1

j

jneth

neth

(3)

where β is a parameter defining the slope of the function. The net activations for the neurons in the output

layer and the outputs are calculated as follows:




5

L

j

jkjkk Iwnetoy0

(4)

where k varies from 1 to M output neurons. The synaptic weights of the interconnections between the hidden

neurons and the output neurons are represented by wkj. The system error is then computed by comparing the

actual outputs (yk) with the desired outputs (dk). The error terms for the output neurons (o

k ) and the hidden

neurons (h

j) are given by:

)()( '

kkk

o

k netoyd (5)

M

k

kj

o

kj

h

j wneth1

' )( (6)

where the sigmoidal activation function is differentiated as follows:

)1())(1)(()(' kkkkk yynetonetoneto

(7)

)1())(1)(()(' jjjjj IInethnethneth (8)

Then, the synaptic weights are updated for each neuron in the hidden layer and the output layer. The

backpropagation algorithm essentially changes synaptic weights along the negative gradient of error energy

function; thus, weight changes are proportional to the magnitude of error energy. The formulations for weight

updates in the output layer and the hidden layer are given as:

)]1()([)()1( twtwItwtw kjkjj

o

kkjkj (9)

)]1()([)()1( tvtvxtvtv jijii

h

jjiji (10)

where η is the learning rate parameter that can be selected from the range [0,1] and α indicates momentum

term varying within [0,1].

In this algorithm, the error energy used for monitoring the progress toward convergence is the

generalized value of all errors that is calculated by the least-squares formulation and represented by a Mean

Squared Error (MSE) as follows (Haykin, 1999):

P M

k

kk ydMP

MSE1 1

21

(11)

where M is the number of neurons in the output layer and P represents the total number of training patterns.

It should be acknowledged that despite their good performance in many situations, ANNs suffer from

a number of shortcomings. In problems where explaining rules may be critical, neural networks are not the




6

tool of choice. They are the tool of choice when acting on the results is more important than understanding

them. Secondly, ANNs usually converge on some solution for any given training set. Unfortunately, there is

no guarantee that this solution provides the best model (global minimum) of the data. Therefore, the test set

must be utilized to determine when a model provides good enough performance to be used on unknown data.

3 Generating ANN training and testing database

The ILLI-PAVE 2000 finite element program was used as the main validated nonlinear structural model for

analysing different geometries of conventional flexible pavements with unbound aggregate bases. The goal

was to establish a database composed of pavement and loading input properties together with the

corresponding ILLI-PAVE response solutions that would eventually constitute the training and testing data

sets needed in the development of ANN-based structural models for the rapid backcalculation analysis of

conventional flexible pavements with unbound aggregate bases.

The top surface asphalt course was characterized as a linear elastic material with Young’s Modulus,

EAC, and Poisson ratio, . Due to its simplicity and ease in model parameter evaluation, the KGB-n model

(Hicks and Monismith, 1971) was used as the nonlinear characterization model for the unbound aggregate

layer. Based on the work of Rada and Witczak (1981) with a comprehensive granular material database,

“KGB” and “n” model parameters can be correlated to characterize the nonlinear stress dependent behavior

with only one model parameter using the following equation (Rada and Witczak, 1981):

nKLog GB 807.1657.410 R2 = 0.68; SEE = 0.22 (12)

According to equation 12, good quality granular materials show higher KGB and lower n values,

whereas the opposite applies for low quality granular materials. For the ILLI-PAVE runs and the ANN

training/testing data generation, the KGB-value ranged from 20.7 MPa (3ksi) to 61.9 MPa (9 ksi) and the

corresponding n-value was obtained using the relationship in equation 12. For Mohr-Coulomb strength

characterization, all granular materials were assumed to have no cohesion (i.e., c = 0), and the friction angle

-values were entered in accordance with the “quality level” of the KGB-value.

Fine-grained soils were considered as “no-friction” but cohesion only materials were modeled using

the bilinear or arithmetic model for modulus characterization (Thompson and Elliott, 1985; Thompson and

Robnett, 1979). The breakpoint deviator stress, ERi, was the main input for subgrade soils.

Therefore, asphalt concrete modulus, EAC, granular base KGB- model parameter KGB, and the

subgrade soil break point deviator stress, ERi, in the bilinear model were used as the layer stiffness inputs for

all the different conventional flexible pavement geometries (i.e., layer thicknesses) analysed using the ILLI-

PAVE 2000 finite element program. The thickness and moduli ranges used are summarized in table 1. The 40-

kN (9-kip) wheel load was applied as a uniform pressure of 552 kPa (80 psi) over a circular area of radius 152

mm (6 in.).




7

Table I. Pavement geometry and material properties used to create ILLI-PAVE finite element solutions.

Material

Type

Layer

Thickness

Material

Model Layer Modulus Inputs Poisson’s Ratio

Asphalt

Concrete

hAC = 76 to

381mm

(3 to 15 in.)

Linear

Elastic

EAC = 0.70 to 13.77 GPa

(100 to 2,000 ksi) = 0.35

Unbound

Aggregate

Base

hGB = 102 to

559 mm

(4 to 22 in.)

Nonlinear

K- model

MR = Kn

“K” = 20.7 to 62 MPa

(3 to 9 ksi)

“n” from equation 12

= 0.35 for K >

34.5 MPa (5 ksi)

= 0.40 for K <

34.5 MPa (5 ksi)

Fine-

grained

Subgrade

7,620 mm

(300 in.)

minus total

pavement

thickness

Nonlinear

Bilinear

Model

MR = f (ERi)

ERi = 6.9 to 96.2 MPa

(1 to 14 ksi) = 0.45

4 Inverse analysis using ANN approach

Backcalculation is the ‘‘inverse’’ problem of determining material properties of pavement layers from its

response to surface loading. No direct, closed-form solution is currently available to determine the layer

moduli of a multilayered system given the surface and layer thicknesses. Most of the existing backcalculation

programs employ iteration or optimization schemes to calculate theoretical deflections by varying the material

properties until a ‘‘tolerable’’ match of measured deflection is obtained. However, in these programs, the

reliability of the solution is dependent upon the seed moduli used as an input. This makes backcalculation an

ill-posed process in which minor deviations between measured and computed deflections usually result in

significantly different moduli. In many cases, various combinations of modulus values essentially produce the

same deflection basin (Mehta and Roque, 2003).

Backpropagation type artificial neural network models were trained in this study with results from the

ILLI-PAVE 2000 finite element model and were used as rapid analysis design tools for predicting pavement

layer moduli and stresses in flexible pavements. Backpropagation ANNs are very powerful and versatile

networks that can be taught a mapping from one data space to another using a representative set of

patterns/examples to be learned. In the development of backpropagation ANN models, the connection weights

and node biases are initially selected at random. Inputs from the mapping examples are propagated forward

through each layer of the network to emerge as outputs. The errors between those outputs and the correct

answers are then propagated backwards through the network and the connection weights and node biases are

individually adjusted to reduce the error. After many examples (training patterns) are propagated through the

network many times, the mapping function is learned with some specified error tolerance. This is called

supervised learning because the network has adjusted functional mapping using the correct answers.

Backpropagation ANNs excel at data modeling with their superior function approximation (Haykin, 1999;

Meier and Tutumluer, 1998; Goktepe et al., 2004).




8

Backpropagation type neural networks were used to develop three ANN structural models with

different network architectures for predicting the pavement layer moduli (EAC, KGB, and ERi) and critical

pavement responses (AC, SG, and D) using the FWD deflection data (see Table 2). The FWD surface

deflections (D0, D8, D12, D18, D24, D36, D48, D60, and D72) are often collected at several different locations, at

the drop location (0-in.) and at radial offsets of 203-mm (8-in.), 254-mm (12-in.), 457-mm (18-in.), 610-mm

(24-in.), 914-mm (36-in.), 1219-mm (48-in.), 1524-mm (60-in.), and 1829-mm (72-in.). For the modeling

work, surface deflections at the FWD sensor radial offsets were obtained from the ILLI-PAVE results. Details

regarding the development of best-performance ANN models employed in the study are presented elsewhere

(Ceylan et al., 2005; Ceylan et al., 2007).

Table II. ANN-Based backcalculation models input parameters and output variables.

ANN

Models Input Parameters

Output

Variables ANN Architecture

BCM-1 hAC, hGB, D0, D12, D24, D36 EAC, ERi 6 – 60 – 60 – 2

BCM-2 hAC, hGB, D0, D8, D12, D24,

D36, D48, D60, D72, EAC, ERi KGB 12 – 60 – 60 – 1

BCM-3 hAC, hGB, D0, D12, D24, D36 AC, SG, D 6 – 60 – 60 – 3

5 Performance of the ANN-based models: Prediction of layer moduli using virgin deflection data

The first backcalculation model BCM-1 was designed to predict EAC of the AC layer and the ERi value of the

subgrade using only four FWD deflections: D0, D12, D24, and D36. The ANN BCM-1 model therefore had 6

input parameters; two layer thicknesses (hAC, hGB), and four FWD pavement surface deflections at 305 mm

(12 in.) spacings (D0, D12, D24, and D36), and 2 output variables of asphalt and subgrade layer moduli, EAC and

ERi. To train the ANN BCM-1, a training data file was formed using the 24,284 ILLI-PAVE runs mentioned

earlier. One thousand of these runs were set aside for use as an independent testing set to check the training

progress and performance of the trained ANN models. Neural network architectures with two hidden layers

were exclusively chosen for the BCM-1 model developed in this study. This was in accordance with the

satisfactory results obtained previously with such networks considering their ability to better facilitate the

nonlinear functional mapping between the input parameters and output variables (Ceylan, 2002).

Several network architectures with two hidden layers were trained for predicting the properties of the

pavement layer moduli with 6 input and 2 output nodes. Overall, the training and testing mean squared errors

(MSEs) decreased as the networks grew in size with increasing number of neurons in the hidden layers until a

certain point and the MSE again increased with increasing number of hidden neurons beyond the optimum

number. The testing MSEs for the two output variables were, in general, slightly lower than the training ones.

The error levels for both the training and testing sets matched closely when the number of hidden nodes

approached 60 as in the case of 6-60-60-2 architecture (6 inputs, 60 and 60 hidden, and 2 output nodes,

respectively).

The development of another backcalculation model ANN BCM-2 was deemed necessary for

accurately predicting the KGB modulus parameter of the KGB-n granular base model. In addition to the layer

thicknesses and FWD surface deflections, the EAC and ERi, already computed from the ANN BCM-1 model,

were used as additional input variables in the BCM-2 model. The BCM-2 network architecture, therefore, had

12 input parameters (hAC, hGB, D0, D8, D12, D24, D36, D48, D60, D72, EAC, and ERi) and a single output variable




9

of KGB value. The best network architecture for the ANN BCM-2 model was also found to have two hidden

layers with 60 hidden nodes in each layer. This 12-60-60-1 ANN BCM-2 model was also trained for 10,000

learning cycles. The trained ANN BCM-2 successfully predicted the KGB values with a low AAE value of

3.53%.

6 Performance of the ANN-based models: Prediction of layer moduli using noisy deflection data

Increasing robustness to noise in ANN based backcalculation models can be described as a generalization

problem: the ANN model is trained on a given training dataset which is synthetically generated (without any

noise) and then applied on different noisy NDT data collected in the field featuring only partially predictable

environmental conditions. Techniques that allow for good prediction performance in spite of differences in

conditions between training and test datasets are sought. Mooney et al. (1989) found that the backpropagation

algorithm is more adaptive to noisy data sets. Since the update rule in the backpropagation algorithm entails

the observation error, the algorithm is quite sensitive to the noisy observations, which directly influence the

value of the adjustable parameter and degrade the learning performance. In this study, a simplified procedure

was employed to artificially introduce noise into the training datasets in pursuit of developing noise-tolerant

ANN backcalculation models.

In addition to the training and testing sets prepared for BCM-1 and BCM-2, six more ANN training

sets were generated by artificially introducing 4% (+2%), 10% (5%) and 20% (10%) noise to the FWD

deflection values used in both backcalculation models. The purpose of introducing noisy patterns in the

training sets was to develop a more robust network that can tolerate the noisy or inaccurate deflection patterns

collected from the FWD deflection basins. Noise was introduced in these networks in the following manner.

The 24,284 ILLI-PAVE solution database was first partitioned to create a training set of 23,284 patterns and

an independent testing set of 1,000 patterns to check the performance of the trained ANN models. A total of

23,284 uniformly distributed random numbers ranging from 0 to 2% and 5% for low-noise levels and

another 23,284 set ranging from 0 to 10% for high-noise patterns were generated each time to create noisy

training patterns. After adding 23,284 randomly selected noise values only to the pavement surface

deflections of D0, D12, D24, and D36, a new training data set was developed for each noisy training set. By

repeating the noise introduction procedure, four more training data sets were formed. Including the original

training set with no noise in it, a total of 116,420 patterns were used to train the noise-introduced ANN

backcalculation models. According to LeCun (1993), each input variable should be preprocessed so that its

mean value, averaged over the entire training set, is close to zero. Thus, inputs were normalized between +2

and -2. In a similar way, outputs were normalized between 0.1 and 0.9 because of the effective ranges of the

sigmoidal activation function considered in the backpropagation type ANN trainings.

The accuracy of the EAC, ERi, and KGB predictions were investigated by comparing the virgin

deflection data results and the noise-introduced deflection data results. As can be seen from figures 1-3, the

average absolute error (AAE) values increase when the noise levels introduced to the deflection data increase.

In these figures, MAE refers to the Mean Average Error.




10

(a) Virgin Data

ILLI-PAVE Asphalt Concrete Moduli, EAC (GPa)

0 4 8 12 16

AN

N A

sph

alt

Con

cret

e M

od

uli

, E

AC

(G

Pa)

0

4

8

12

16AAE = 1.22 %

Line of Equality

MAE = 0.63 GPa

(c) + 5 Noisy Data


0 4 8 12 16

AN

N A

sph

alt

Co

ncr

ete

Mo

du

li, E

AC

(G

Pa

)

0

4

8

12

16AAE = 4.85 %

Line of Equality

MAE = 1.60 GPa

(b) + 2 Noisy Data


0 4 8 12 16

AN

N A

sph

alt

Con

cret

e M

od

uli

, E

AC

(G

Pa)

0

4

8

12

16AAE = 2.77 %

Line of Equality

MAE = 1.30 GPa

(d) + 10 Noisy Data


0 4 8 12 16

AN

N A

sph

alt

Co

ncr

ete

Mo

du

li, E

AC

(G

Pa

)

0

4

8

12

16AAE = 7.41 %

Line of Equality

MAE = 2.09 GPa

Figure 1. Accuracy of the asphalt concrete modulus (EAC) predictions for varying noise levels.




11

(a) Virgin Data

ILLI-PAVE Subgrade Moduli, ERi (MPa)

0 30 60 90 120

AN

N S

ub

grad

e M

odu

li, E

Ri

(MP

a)

0

30

60

90

120AAE = 3.27 %

Line of Equality

MAE = 11.93 MPa

(b) + 2 Noisy Data


0 30 60 90 120

AN

N S

ub

gra

de

Mo

du

li, E

Ri

(MP

a)

0

30

60

90

120AAE = 5.19 %

Line of Equality

MAE = 11.83 MPa

(c) + 5 Noisy Data


0 30 60 90 120

AN

N S

ub

grad

e M

odu

li, E

Ri

(MP

a)

0

30

60

90

120AAE = 6.57 %

Line of Equality

MAE = 15.31 MPa

(d) + 10 Noisy Data


0 30 60 90 120

AN

N S

ub

grad

e M

odu

li, E

Ri

(MP

a)

0

30

60

90

120AAE = 8.03 %

Line of Equality

MAE = 18.89 MPa

Figure 2. Accuracy of the subgrade layer modulus (ERi) predictions for varying noise levels.




12

(a) Virgin Data

ILLI-PAVE KGB

(MPa)

20 40 60

AN

N K

GB (

MP

a)

20

40

60

AAE = 3.53%

Line of Equality

MAE = 8.12 MPa

(b) + 2 Noisy Data

ILLI-PAVE KGB

(MPa)

20 40 60

AN

N K

GB (

MP

a)

20

40

60

AAE = 10.04%

Line of Equality

MAE = 40.90 MPa

(c) + 5 Noisy Data

ILLI-PAVE KGB

(MPa)

20 40 60

AN

N K

GB (

MP

a)

20

40

60

AAE = 15.62%

Line of Equality

MAE = 33.05 MPa

(d) + 10 Noisy Data

ILLI-PAVE KGB

(MPa)

20 40 60

AN

N K

GB (

MP

a)

20

40

60

AAE = 22.12%

Line of Equality

MAE = 36.29 MPa

Figure 3. Accuracy of the granular base modulus (KGB) predictions for varying noise levels.




13

7 Performance of the ANN-based models: Prediction of critical pavement responses using virgin

deflection data

A different backcalculation model, ANN BCM-3, was developed for predicting the critical pavement

responses, AC, SG, and D, directly from the FWD deflection data. This approach eliminates the need of first

predicting the pavement layer moduli and then using a forward calculation structural analysis model to

compute the critical pavement responses needed for mechanistic based pavement analysis and design. The

directness of this approach can save time and effort in analyzing structural adequacy of field pavement

sections such as the direct use of predicted AC for AC fatigue condition evaluation. After studying several

different network architectures, it was once again deemed necessary to consider 60 hidden neurons in each

hidden layer and accordingly, the 6-60-60-3 network architectures were trained for 10,000 learning cycles to

obtain the lowest training and testing MSEs.

8 Performance of the ANN-based models: Prediction of critical pavement responses using noisy

deflection data

In addition to the training and testing sets prepared for BCM-3 model, three more ANN training sets were

generated by introducing 4% (2%), 10%(5%) and 20% (10%) noise to the FWD deflection values used in

BCM-3 model.

The accuracy of the AC, SG, and D predictions were investigated by comparing the virgin deflection

data results and the noise-introduced deflection data results. As can be seen from figures 4-6, the AAE values

increase when the noise levels introduced to the deflection data increase.

(a) Virgin Data

ILLI-PAVE Asphalt

Concrete Strain, eAC (m)

0 200 400 600

AN

N A

sph

alt

Co

ncr

ete

Str

ain

, eA

C (

m)

0

200

400

600AAE = 0.46 %

Line of Equality

MAE = 15.16 mm

(b) + 2 Noisy Data

ILLI-PAVE Asphalt


0 200 400 600

AN

N A

sph

alt

Con

cret

e

Str

ain

, eA

C (

m)

0

200

400

600AAE = 0.76 %

Line of Equality

MAE = 25.82 mm




14

(c) + 5 Noisy Data

ILLI-PAVE Asphalt


0 200 400 600

AN

N A

sph

alt

Con

cret

e

Str

ain

, eA

C (

m)

0

200

400

600AAE = 1.76 %

Line of Equality

MAE = 31.40 mm

(d) + 10 Noisy Data

ILLI-PAVE Asphalt


0 200 400 600

AN

N A

sph

alt

Con

cret

e

Str

ain

, eA

C (

m)

0

200

400

600AAE = 3.34 %

Line of Equality

MAE = 35.17 mm

Figure 4. Accuracy of the asphalt concrete strain AC) predictions for varying noise levels.

(a) Virgin Data

ILLI-PAVE Subgrade

Strain, eSG (m)

0 800 1600 2400

AN

N S

ub

gra

de

Str

ain

, e S

G (

m)

0

800

1600

2400AAE = 2.03 %

Line of Equality

MAE = 28.30 mm

(b) + 2 Noisy Data

ILLI-PAVE Subgrade

Strain, eSG (m)

0 800 1600 2400

AN

N S

ub

gra

de

Str

ain

, e S

G (

m)

0

800

1600

2400AAE = 4.74 %

Line of Equality

MAE = 40.11 mm




15

(c) + 5 Noisy Data

ILLI-PAVE Subgrade

Strain, eSG (m)

0 800 1600 2400

AN

N S

ub

gra

de

Str

ain

, e S

G (

m)

0

800

1600

2400AAE = 4.92 %

Line of Equality

MAE = 85.20 mm

(d) + 10 Noisy Data

ILLI-PAVE Subgrade

Strain, eSG (m)

0 800 1600 2400

AN

N S

ub

gra

de

Str

ain

, e S

G (

m)

0

800

1600

2400AAE = 5.27 %

Line of Equality

MAE = 99.81 mm

Figure 5. Accuracy of the subgrade strain (SG) predictions for varying noise levels.

(a) Virgin Data

ILLI-PAVE Subgrade

Deviator Stress, sD (kPa)

0 20 40 60 80

AN

N S

ub

gra

de

Dev

iato

r S

tres

s, s

D (

kP

a)

0

20

40

60

80AAE = 1.36 %

Line of Equality

MAE = 1.63 kPa

(b) + 2 Noisy Data

ILLI-PAVE Subgrade


0 20 40 60 80

AN

N S

ub

gra

de

Dev

iato

r S

tres

s, s

D (

kP

a)

0

20

40

60

80AAE = 1.90 %

Line of Equality

MAE = 1.71 kPa




16

(c) + 5 Noisy Data

ILLI-PAVE Subgrade


0 20 40 60 80

AN

N S

ub

gra

de

Dev

iato

r S

tres

s, s

D (

kP

a)

0

20

40

60

80AAE = 2.42 %

Line of Equality

MAE = 1.55 kPa

(d) + 10 Noisy Data

ILLI-PAVE Subgrade


0 20 40 60 80

AN

N S

ub

grad

e

Devia

tor S

tress

, s

D (

kP

a)

0

20

40

60

80AAE = 4.07%

Line of Equality

MAE = 3.17 kPa

Figure .6 Accuracy of the deviator stress (D) predictions for varying noise levels.

9 Discussion of results

In this section, the results of the robust (noise-introduced) ANN trainings were compared with the results from

ANN models trained with the virgin data sets. In addition to these models, robust network architectures were

trained with varying levels of noise introduced to the asphalt concrete layer thickness data.

9.1 Average Absolute Error (% AAE) variations

Average absolute error (AAE) variations in asphalt concrete moduli predictions were investigated. The

minimum AAEs were obtained in the trainings that used virgin deflection data. As seen from figure 7, when

the level of noise (%) introduced to the deflection data increased, the AAE value also increased as expected.

The highest increase in AAE value was found in the KGB predictions with the introduction of noise in the

deflection data.

Also, AAE (%) variations for the critical pavement response predictions were investigated. Similar

trends were observed for critical pavement response prediction AAEs as in the case of pavement layer moduli

prediction AAEs, i.e., increase in AAE with increase in noise level (see figure 8).




17

AAE (%) Variation for the Elastic Moduli Predictions

0

5

10

15

20

25

Virgin Def. +2% Noisy Def. +5% Noisy Def. +10% Noisy Def.

AA

E (

%)

EAC 1.22 2.77 4.85 7.41

ERI 3.27 5.19 6.57 8.03

KGB 3.53 10.04 15.62 22.12

1 2 3 4

Figure 7. Variations of average absolute error (AAE) values for predicting the asphalt layer moduli for

different noise levels.

AAE (%) Variation for the Critical Pavement

Responses Predictions

0

1

2

3

4

5

6

Virgin Def. +2% Noisy Def. +5% Noisy Def. +10 Noisy Def.

AA

E (

%)

Strain AC 0.46 0.76 1.76 3.34

Strain SG 2.03 4.74 4.92 5.27

Dev.Stress. 1.36 1.9 2.42 4.07

1 2 3 4

Figure 8. Variations of average absolute error (AAE) values for predicting the critical pavement responses for

different noise levels.




18

9.2 Moduli predictions results with simultaneous introduction of noise in deflection and layer thickness

data

Previously, the noise was introduced only to the deflection data but not to the layer thickness data. In this part

of the study, the noise was also introduced to the layer thicknesses and the results were compared. The

comparison was conducted only for the asphalt concrete elastic modulus predictions by introducing + 5%

noise to the both deflections and layer thicknesses. The results are presented in figure 9. As seen from the

figure, the AAE (%) value has increased when the noise was also introduced to the layer thicknesses, as

expected.

(a) + 5 Noisy (Only Deflection) Data


0 4 8 12 16

AN

N A

sph

alt

Co

ncrete

M

od

uli

, E

AC

(G

Pa

)

0

4

8

12

16

AAE = 4.85 %

Line of Equality

(b) + 5 Noisy (Deflection + Thickness) Data


0 4 8 12 16

AN

N A

sph

alt

Con

crete

M

od

uli

, E

AC

(G

Pa

)

0

4

8

12

16

AAE = 5.14 %

Line of Equality

Figure 9. Effect of noise introduction on the asphalt concrete layer thickness.

9.3 Results for the noise-introduced testing data set

Previously, the noise was introduced only to the training data set but not to the test data set. In this part of the

study, the noise was also introduced to the test data set and the results were compared. For the sake of

simplicity, + 5% noise was introduced to the both training and testing data set and the comparison was

conducted only for the asphalt concrete elastic modulus predictions. The results are presented in figure 12. As

seen from figure 10, the AAE value for the AC moduli predictions using the testing data set increased from

4.85% to 8.28% when the noise was also introduced to the testing data set. In figure 11, the progress curves

for the noisy training data set and noisy testing data sets are presented. As expected, when the noise was also

introduced to the testing data set, mean squared error values (MSE) for the testing data set were very close to

the MSE obtained for the training data set.




19

(a) + 5 Noisy Data (TRN)


0 4 8 12 16

AN

N A

sph

alt

Con

cret

e M

od

uli

, E

AC

(G

Pa)

0

4

8

12

16

AAE = 4.85 %

Line of Equality

(b) + 5 Noisy Data (TRN+TST)


0 4 8 12 16

AN

N A

sph

alt

Con

crete

M

od

uli

, E

AC

(G

Pa)

0

4

8

12

16

AAE = 8.28 %

Line of Equality

Figure 10. Effect of noise introduction on the asphalt concrete layer moduli testing data.

EAC, +5% Noisy Data (TRN)

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

0 2000 4000 6000 8000 10000 12000

Learning Cycles (Epochs)

Mean

Sq

uare

d E

rro

r (M

SE

)

Training Set

Testing Set

(a) Learning Cycles (Epochs)




20

EAC, + 5% Noisy Data (TRN+TST)

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

0 2000 4000 6000 8000 10000 12000

Learning Cycles (Epochs)

Mean

Sq

uare

d E

rro

r (M

SE

)

Training Set

Testing Set

(b) Learning Cycles (Epochs)

Figure 11. Comparison of the training and testing progress curves curves. (a) EAC predictions with + 5% noise

in the training (TRN) data set and (b) EAC predictions with + 5% noise in the training (TRN) and testing

(TST) data sets.

10 Summary and conclusions

Structural evaluation and rehabilitation of the existing road and airport infrastructure requires development of

inexpensive and reliable techniques for non-destructive testing and evaluation of pavement systems. Many

researchers have indicated that stiffness determined through nondestructive testing is a fundamental method of

determining effective layer moduli. The main objective of this study was to employ biologically inspired

computational systems to develop robust pavement layer moduli backcalculation algorithms that can tolerate

noise or inaccuracies in the falling weight deflectometer (FWD) deflection data collected in the field.

Artificial neural network (ANN) models were developed to perform rapid and accurate predictions of

flexible pavement layer moduli and critical pavement responses from FWD deflection basins for a number of

pavement input parameters considered in analysis and design. Three ANN backcalculation models were

developed using approximately 24 thousand nonlinear ILLI-PAVE finite element solutions. Unlike the linear

elastic layered theory commonly used in pavement layer backcalculation, realistic nonlinear unbound

aggregate base (UAB) and subgrade soil response models were used in the ILLI-PAVE finite element

program to account for the typical hardening behavior of UABs and softening nature of fine-grained subgrade

soils under increasing stress states. The virgin and the varying levels of noise-introduced (robust) ANN

models developed in this study successfully predicted the pavement layer moduli and critical pavement

responses obtained from the ILLI-PAVE finite element solutions and are considered superior to the linear

elastic layered backcalculation analyses due to the nonlinear material characterization employed. Varying




21

levels of noise was also introduced to the pavement layer thicknesses and the testing data set to investigate the

performance of the noise introduced ANN models.

Such ANN structural analysis models can provide pavement engineers and designers with

sophisticated finite element solutions, without the need for a high degree of expertise in the input and output

of the problem, to rapidly analyze a large number of pavement sections and FWD deflection basins needed for

routine pavement evaluation. Noise introduced ANN models were found to be more robust compared to the

models trained with the virgin training data. Such ANN models provide more realistic layer moduli and

critical pavement responses because of their ability to tolerate the inaccuracies in the pavement deflection

basins and the layer thicknesses due to poor construction practices. The use of the ANN models also resulted

in both a drastic reduction in computation time (about 0.35 million times faster than the finite element model)

and a simplification of the complicated finite element program input and output requirements.

11 References

AASHTO T307-99 (2000), “Determining the resilient modulus of soils and aggregate materials.” Standard

Specifications for Transportation Materials and Methods of Sampling and Testing, 20th Edition, AASHTO,

Washington D.C.

Bredenhann, S. J. and M.F.C. van de Ven (2004). ”Application of aritificial neural networks in the back-

calculation of flexible pavement layer moduli from deflection measurements”. Proceedings of the 8th

Conference on Asphalt Pavements for Southern Africa (CAPSA’04), Sun City, South Africa.

Brown, S.F., and Pappin, J.W. (1981), “Analysis of pavements with granular bases.” In Transportation

Research Record 810, TRB, National Research Council, Washington, D.C., pp. 17-23.

Ceylan, H. (2002), “Analysis and design of concrete pavement systems using artificial neural networks.” Ph.D.

Dissertation, University of Illinois at Urbana-Champaign, December.

Ceylan, H., E. Tutumluer, and E.J. Barenberg (1998), “Artificial Neural Networks as Design tools in Concrete

Airfield Pavement Design,” Proceedings of the 25th ASCE international Air Transportation Conference,

Austin, TX. America Socirty of Civil Engineers (ASCE), Reston, VA, pp. 447-465.

Ceylan, H., Guclu, A., Tutumluer, E. and Thompson, M.R. (2005). “Backcalculation of Full-Depth Asphalt

Pavement Layer Moduli Considering Nonlinear Stress-Dependent Subgrade Behavior”. The Int. J. of

Pavement Engrg., 6(3), pp. 171-182.

Ceylan, H., Guclu, A., Tutumluer, E., and Thompson, M. R. (2007). “Nondestructive Evaluation of Iowa

Pavements-Phase I.” Final Report, CTRE Project 04-177, Center for Transportation Research and

Education (CTRE), Iowa State University, Ames, IA.

Duncan, J.M., Monismith, C.L., and Wilson, E.L. (1968), “Finite element analyses of pavements.” In

Highway Research Record No. 228, HRB, National Research Council, Washington D.C.

European CEN Std EN 13286-7 (2003), “Unbound and hydraulically bound mixtures - Test methods – Part 7:

Cyclic load triaxial test for unbound mixtures.” European Standard, European Committee for

Standardization, European Union.

Garg, N., Tutumluer, E., and Thompson, M.R. (1998), “Structural modeling concepts for the design of airport

pavements for heavy aircraft.” Proceedings, Fifth International Conference on the Bearing Capacity of

Roads and Airfields, Trondheim, Norway, July 1998.

Goktepe, B., E. Agar, and A. H. Lav (2004). “Comparison of Multilayer Perceptron and Adaptive Neuro-

Fuzzy System on Backcalculating the Mechanical Properties of Flexible Pavements,” ARI: The Bulletin of

the Istanbul Tech. Univ., 54 (3), pp. 65-77.




22

Gomez-Achecar, M., and Thompson, M.R. (1986), “ILLI-PAVE based response algorithms for full depth

asphalt concrete pavements.” In Transportation Research Record No. 1095, TRB, National Research

Council, Washington D.C., pp. 11-18.

Gomez-Ramirez, F., Thompson, M.R., and Bejarano, M. (2002), “ILLI-PAVE based flexible pavement design

concepts for multiple wheel heavy gear load aircraft.” In Proceedings of the 9th

International Conference

on Asphalt Pavements, Copenhagen, Denmark.

Gucunski, N. and Krstic, V. (1996), “Backcalculation of pavement profiles from spectral-analysis-of-surface

waves test by neural networks using individual receiver spacing approach.” In Transportation Research

Record No. 1526, TRB, National Research Council, Washington, D.C., pp. 6-13.

Haas, R., R. W. Hudson, and J. P. Zaniewski (1994). Modern Pavement Management, Krieger Publishing Co.,

Malabar, FL, USA.

Haykin, S. (1999), “Neural networks: A comprehensive foundation.” Prentice-Hall, Inc, Englewood

Cliffs, NJ, USA.

Hicks, R.G., and C.L. Monismith, (1971), “Factors influencing the resilient properties of granular materials.”

In Transportation Research Record No. 345, TRB, National Research Council, Washington D.C., pp. 15-31.

Khazanovich, L., and Roesler, J. (1997), “DIPLOBACK: Neural-network-based backcalculation program for

composite pavements.” In Transportation Research Record No. 1570, TRB, National Research Council,

Washington, D.C., pp. 143-150.

Kim, Y., and Kim R.Y. (1998), “Prediction of layer moduli from falling weight deflectometer and surface

wave measurements using artificial neural network.” In Transportation Research Record No. 1639, TRB,

National Research Council, Washington, D.C., pp. 53-61.

LeCun, Y.(1993), Efficient learning and second-order methods, a tutorial at NIPS 93, Denver, CO, Morgan

Kaufmann, San Francisco, CA.

Macdonald, R. A. (2002). “Pavement Technology Project in Thailand. Road Directorate,” Danish Road

Institute, Report No. 119, Denmark.

Mehta, Y. and R. Roque (2003). “Evaluation of FWD data for determination of layer moduli of pavements”.

Journal of Materials in Civil Engineering, ASCE, Vol. 15, No. 1, pp. 25-31.

Meier, R. and Tutumluer, E. (1998), “Uses of artificial neural networks in the mechanistic-empirical design of

flexible pavements.” In Proceedings of the International Workshop on Artificial Intelligence and

Mathematical Methods in Pavement and Geomechanical Engineering Systems, Florida International

University, Miami, FL, pp. 1-12.

Meier, R.W. and Rix, G.J. (1995), “Backcalculation of flexible pavement moduli from dynamic deflection

basins using artificial neural networks.” In Transportation Research Record No. 1473, TRB, National

Research Council, Washington, D.C., pp. 72-81.

Meier, R.W., Alexander, D.R., and Freeman, R. (1997), “Using artificial neural networks as a forward

approach to backcalculation.” In Transportation Research Record No. 1570, TRB, National Research

Council, Washington, D.C., pp. 126-133.

Mooney, R., Shavlik, R., Towell, G., and Gove, A. (1989). “An experimental comparison of symbolic and

connectionist learning algorithms. “ In Proceedings of the Eleventh International Joint Conference on

Artificial Intelligence (IJCAI-89), Detroit, MI, August 20-25, pp. 775-780.

Parker, D.B. (1985), “Learning logic.” Technical Report TR-47, Center for Computational Research in

Economics and Management Science, Massachusetts Inst. of Technology, Cambridge, MA, USA

Raad, L., and Figueroa, J.L. (1980), “Load response of transportation support systems.” Transportation

Engineering Journal, ASCE, Vol. 16, No. TE1, pp. 111-128.




23

Rada, G., and Witczak, M.W. (1981), “Comprehensive evaluation of laboratory resilient moduli results for

granular material.” In Transportation Research Record No. 810, TRB, National Research Council,

Washington D.C., pp. 23-33.

Rumelhart, D.E., Hinton, G.E., and Williams, R.J. (1986), “Learning representations by back-propagating

errors.” Nature, Vol. 323, pp. 533-536.

Thompson, M.R. (1992), “ILLI-PAVE based conventional flexible pavement design procedure.” In

Proceedings of the 7th

International Conference on Asphalt Pavements, Nottingham, U.K.

Thompson, M.R., and Elliott, R.P. (1985), “ILLI-PAVE based response algorithms for design of conventional

flexible pavements.” In Transportation Research Record No. 1043, TRB, National Research Council,

Washington, D.C., pp. 50-57.

Thompson, M.R., and Robnett, Q.L. (1979), “Resilient properties of subgrade soils.” Transportation

Engineering Journal. ASCE. Vol. 105, No. TE1, pp. 71-89.

Trentin, E. and Matassoni, M. (2003), “Noise-tolerant speech recognition: the SNN-TA approach”.

Information Sciences: An International Journal, Vol. 156, pp. 55-69

Uzan, J. (1985), “Characterization of granular materials.” In Transportation Research Record No. 1022, TRB,

National Research Council, Washington D.C., pp. 52-59.

Uzan, J., Witczak, M.W., Scullion, T., and Lytton, R.L. (1992), “Development and validation of realistic

pavement response models.” In Proceedings of the 7th

International Conference on Asphalt Pavements,

Nottingham. International Society for Asphalt Pavements (ISAP), Lino Lakes, MN, Vol. 1, pp. 334-350.

Werbos, P. (1974), “Beyond regression: New tools for prediction and analysis in the behavioral sciences.”

Ph.D. Dissertation, Harvard University, MA, USA.

Date post:	22-Mar-2020
Category:	Documents
Upload:	others
View:	11 times
Download:	0 times

Noise-tolerant inverse analysis models for nondestructive ... · Noise-tolerant inverse analysis...

Documents