ann prediction model for composite plates against low velocity impact loads using finite element...

Composite Structures 101 (2013) 290–300

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Composite Structures

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ANN prediction model for composite plates against low velocity impact loadsusing finite element analysis

M.H. Malik, A.F.M. Arif ⇑King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

a r t i c l e i n f o

Article history:Available online 27 February 2013

Keywords:Composite platesImpact resistanceDesign of experimentsFinite element analysisArtificial Neural NetworksCarbon/epoxy plates

0263-8223/$ - see front matter � 2013 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.compstruct.2013.02.020

⇑ Corresponding author. Address: Bldg-22 Room-2Petroleum and Minerals, Dhahran 31261, Saudi Arabi

E-mail address: [email protected] (A.F.M. Arif

a b s t r a c t

In this paper, the use of Artificial Neural Networks to predict the absorbed energy in the composite platesimpacted with low velocity is described. The impact response of a composite laminate depends upon var-ious factors such as thickness, stacking sequence and number of layers. These factors are identified in anearlier study using the sensitivity analysis. These factors have the most prominent effect on the impactresistance of the composite plates. These are studied here with the help of design of experiments so thata suitable data set is obtained. The ability to solve a large number of simulations using FEA gives anadvantage in the design optimization with the help of DOE (Design of Experiments). During the study dif-ferent variations of these factors were tried and the response in terms of the absorbed energy was esti-mated. The simulation results were then used along with the ANN (Artificial Neural Networks) to fit afunction to estimate the amount of absorbed energy. The results from the DOE follow the intuition thatthe increase of thickness and number of layers increase the performance of the composite plates. TheANN model is trained such that it is able to predict with an acceptable accuracy range the amount ofabsorbed energy for different configurations of input variables. The paper discusses the codification ofinput variables so that they can be used to train ANN model. Also, the use of differential evolution algo-rithm is discussed which is used to select the best possible ANN model based on the maximum error androot mean square error of the ANN models.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Fiber reinforced polymers have been in use in a variety of appli-cations from medical to engineering structures. These structuresare designed to withstand loads that conventional metals cannothold without putting the weight penalty due to their highstrength-to-weight and stiffness-to-weight ratios [29]. Most ofthese structures are designed to take loads such as tensile loadsand internal pressure, but during operational life they encounterimpact loads as well. The impact behavior of metals is well definedand can be predicted accurately, however fiber reinforced compos-ites are quite complex in behavior with regards to impact loadswhich can result in internal damages and loss of stiffness but thedamage is often unobservable during visual inspection [1]. The im-pact loads results usually in delamination, fiber breakage and ma-trix cracking [9], the damage mechanics in fiber reinforcedpolymeric composites is different than conventional metals andis because of the different layered configuration and presence ofheterogeneous materials. A number of studies have been per-formed to study the behavior of composite plates, the studies are

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experimental [4,8,11,14,28,30,31,33], numerical [5,16,17,31] andanalytical [12] which discuss the impact behavior of different com-posite laminates. These studies mainly focused on the develop-ment of analytical and numerical methods to understand theimpact behavior of the composite plates under low velocity im-pacts. These include the studying the effects of various parameterson the impact response of the composite plates. Hosseinzadehet al. [11] studied the effects of different materials and energy lev-els, while Menna et al. [23] discussed the effect of thickness at var-ious impact energies for glass/epoxy fabric laminates. Cantwell [8]studied the effects of geometry on the impact response of glass fi-ber reinforced composites and Karakuzu et al. [14] discussed theeffects of impactor mass and velocity have on the impact charac-teristics of glass/epoxy composites. Similarly, Mikkor et al. [24]studied the effects on the carbon/epoxy composite system andthe effects of preload, impact velocity and geometry of the speci-men. Naik and Meduri [26] investigated the impact behavior ofwoven-fabric laminated composite plates and the effect of the fab-ric geometry and the effect of unidirectional at two different im-pact velocities. Aktas et al. [2] studied the different damagemodes and the effect of different stacking sequence were studiedunder different impact energies.

The literature available provided an insight into how the vari-ous factors affect the impact response of the composite plates.

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Nomenclature

E11 elastic modulus in longitudinal direction [N/m2]E22 elastic modulus in transverse direction [N/m2]E33 elastic modulus in transverse direction [N/m2]m12 Poisson’s ratio in plane containing fiber [unitless]m13 Poisson’s ratio in plane containing fiber [unitless]m23 Poisson’s ratio in transverse plane [unitless]G12 shear modulus in plane containing fiber [N/m2]G13 shear modulus in plane containing fiber [N/m2]G23 shear modulus in transverse plane [N/m2]Xt tensile strength in fiber direction [N/m2]Xc compressive strength in fiber direction [N/m2]Yt tensile strength in transverse direction [N/m2]Yc compressive strength in transverse direction [N/m2]S12 in-plane shear strength [N/m2]

Gtf fracture toughness in longitudinal tensile direction [J/

m2]Gc

f fracture toughness in longitudinal compressive direc-tion [J/m2]

Gtm fracture toughness in transverse tensile fracture mode

[J/m2]Gc

m fracture toughness in transverse compressive fracturemode [J/m2]

Gs in-plane fracture toughness [J/m2]NSC normalized sensitivity coefficient [unitless]Tp thickness of layersSt stacking sequenceN number of layers

M.H. Malik, A.F.M. Arif / Composite Structures 101 (2013) 290–300 291

The optimization of composite plates against the impact loads isone of the primary concerns for the designers especially in theapplications where during operation; structures are susceptibleto impact damages such as the aircrafts, automobile parts and openair pipelines. The impact response for composite materials is notvery well documented and hence novel optimization techniqueslike ANN (Artificial Neural Networks) along with other optimiza-tion techniques such as GA (Genetic Algorithm) are introduced.ANN models are a very powerful method since they can be appliedto any generic problem with few inputs and can be trained to learnfrom them with the expected outputs. ANN models proved to beexcellent tool in the approximation and interpolation in a varietyof applications [6,7,10,13,15,18,19,21,22,27,32,34]. ANN has beenused in function fitting and prediction of various mechanical prop-erties and damage mechanisms in composite materials. Bezerraet al. [7] used ANN to predict the shear stress–strain behavior ofcarbon/epoxy and glass/epoxy fabric composites. The authors usedthe multi-layered neural network model and demonstrated that

Fig. 1. Flow chart of the pro

about 80% of standard error of prediction was P0.9. In their study,they considered the stress as a function of the orientation angle bylayers, specimen of fiber and the shear strain, while certain otherfactors like porosity, number of layers, matrix type and volumetricfraction of fibers were not studied. Vassilopoulos et al. [32] usedANN to model the fatigue life of multidirectional GFRP compositelaminates. The benefit that ANN provided the authors was the ap-proach saved around 50% experimental effort for the whole analy-sis as compared to conventional methods and that too without theloss of considerable accuracy. Jiang et al. [13] applied the ANNmodel to predict the mechanical and wear properties of the shortfiber reinforced polyamide composites. The polyamide compositeswere reinforced by short carbon and glass fibers and then optimi-zation of the neural networks was performed. The neural networkwas used to predict the mechanical and wear properties as a func-tion of the content of fibers and testing conditions.

In this present work, a DOE approach is applied to generate thedata to simulate experiments and generate data set for the ANN

cess for ANN modeling.

Fig. 3. Layup plot and material orientation.

292 M.H. Malik, A.F.M. Arif / Composite Structures 101 (2013) 290–300

model to be applied upon in order to approximate and interpolatefor the future application of optimization algorithms. In this work,three factors were used to draw up the DOE table with initially fullfactorial experiments and then later on added random experimentsto create a larger data set to use with ANN model for two differentfiber materials. Since, the ANN technique is developed in order tooptimize the composite plate in the further studies, it was impor-tant to include all the cases from the complete penetration of theimpactor in the plate to the configuration where there will be min-imum damage occurring in the specimens. In this study, differentvariations of neural networks were studied by the authors and adifferential evolution algorithm was applied to get the best neuralnetwork in terms of neurons and number of layers so that the over-all error is reduced. In Fig. 1, the flow of the whole process is dem-onstrated. The process starts with the FEM model and its validationand involves certain inevitable steps like the training and testing ofthe ANN model. In the subsequent sections, these modules will bediscussed with appropriate details.

2. FE Model and validation

For the purpose of this study, the data required to train ANNmodels was collected through numerical simulations using com-mercial FEA software ABAQUS explicit. As it is a common practicein numerical studies, the numerical model had to be validatedagainst already verified numerical or experimental results. There-fore, a numerical model was chosen from the study of Yokoyamaet al. [35], the study by Yokoyama et al. was based upon experi-mental and numerical results. The experimental results were basedupon the thesis of Biase EHC., and also presented in the study ofYokoyama et al., and the same model was developed in the ABA-QUS to verify the model.

The geometric dimensions of the composite plate and theimpactor and also the stacking sequence of the plate are provided

Table 1Geometric dimensions of the composite plate and impactor.

Composite plate Impactor

Length 102 mm Diameter 12.7 mmWidth 152 mm Mass 1.5 kgThickness 4.2 mm Velocity 6.0608 m/s

Fig. 2. (a) Model showing the length and height of the plate and

in Table 1. Fig. 2 represents the meshing of the composite plate andthe shape of impactor and Fig. 3 shows the ply configuration. Thematerial considered in the analysis is a woven fabric of either car-bon/epoxy system or glass/epoxy system, for validation howevercarbon/epoxy composite plates were used. The geometry of thecomposite plate is 2-D which is meshed using the S4R shell ele-ments; the load is applied in the form of initial velocity to theimpactor which equates to 27.55 J of energy at the time of impact.The boundary conditions are considered to be rigid fixed at the twoshorter ends, since the model is simplified using quarter symme-try; symmetric boundary conditions have been applied as wellon the appropriate edges of symmetry.

The results reported in the study by Yokoyama et al. [35] areused to validate the results. Our study reveals a much closer resultto the experimental values.

In the Table 2, the results are shown for the experimental andnumerical results from the previous studies for both the Hashinmodel and the model proposed by Yokoyama et al. and comparedwith our results using the Hashin model. Fig. 4 gives the time his-tory plot of displacement of the center node of the plate and com-pares the results from all the reported results from Yokoyama et al.[35] with the results from this study. Fig. 5 shows the contour plotof the displacement at the time of maximum contact where the ki-netic energy of the impactor became zero.

the mesh of the plate and (b) the impactor as a rigid solid.

Table 2Results from Yokoyama et al. and the comparison with our results.

Experimental(Yokoyama) [35]

Numerical(Yokoyama-Proposed Model) [35]

Numerical(Yokoyama-Hashin Model) [35]

Current Result Error (%age)

Maximum displacement (m) 0.006018 0.00611 0.00592 0.006062 0.7Time of impact event 0.0036 0.00354 0.00328 0.00338 6.1

Fig. 4. Maximum displacement for the composite plate with respect to time. Experimental and numerical results for displacement–time curve from Yokoyama et al. [35].

Fig. 5. Displacement contour at the instant of 1.6 ms coincident with zero kineticenergy of impactor.

Table 3Sorted list of the parameters according to normalized sensitivity coefficient (NSC).

No. Symbol Energy absorbed inX + DX (J)

Energy absorbed inX � DX (J)

NSC

X1 Tp 4.59 5.16 1.4096X3 St 5.59 5.34 0.2899X10 Xt 4.66 4.87 0.2001X2 N 4.77 4.88 0.0609X15 Gt

f4.70 4.81 0.0479

X5 E22 = E33 4.80 4.70 0.0440X4 E11 4.77 4.72 0.0117X6 m12 = m13 4.78 4.75 0.0056X16 Gc

f 4.74 4.77 0.0042

X8 G12 = G13 4.74 4.76 0.0024X11 Xc 4.77 4.75 0.0015X17 Gt

m4.76 4.74 0.0014

X13 Yc 4.77 4.75 8.22 � 10�4

X14 S12 4.74 4.75 3.89 � 10�4

X12 Yt 4.75 4.76 3.35 � 10�4

X18 Gcm 4.76 4.76 1.69 � 10�4

X7 m23 4.76 4.76 1.28 � 10�4

X9 G23 4.74 4.73 6.4 � 10�6


3. Sensitivity analysis

In a previous study by the authors [20], a sensitivity analysiswas performed in order to investigate the effects of various mate-rial and geometric properties on the impact performance of thecomposite plates. The factors considered to have an effect on theimpact performances are listed in Table 3 along with the normal-ized sensitivity coefficients (NSCs) calculated for each case. Theoutput variable for sensitivity analysis is chosen to be the dissi-pated impact energy or the energy absorbed during the impact

event. The validated model was selected as the nominal case andthe amount of absorbed energy for the nominal case was foundto be 4.74 J.

This study demonstrated the important factors upon which theimpact resistance of a composite plate depends. The values of theNSC for these factors are plotted in Fig. 6, where it can be observedthat the values of NSC for factors such as thickness, tensile strengthetc. is considerably higher than others. Based on these results, astudy using design of experiments is carried out with the factorsconsidered are:

(1) Thickness of each layer/ply.(2) Stacking Sequence.(3) Tensile strength in the fiber direction.(4) Number of layers.(5) Fracture toughness in the fiber direction during tensile

loading.

Fig. 6. NSC for all the variables demonstrating the relative effect of each on theabsorbed impact energy.

Table 5DOE table for GFRP plates.

Thickness (mm) Number of layers Stacking sequence

Factors Levels Factors Levels Factors Levels

0.25 1 24 1 [0/30/60/90] 10.3 2 28 2 [45/�45/0/90] 20.35 3 32 3 [45/30/�30/�45] 30.4 4 36 4 [60/45/�45/�60] 40.45 50.5 60.6 7

Table 6Material properties of the composite materials used in the study.

Carbon/epoxy Glass/epoxy

Elastic propertiesE1 (GPa) 60.8 26E2 (GPa) 58.25 26E3 (GPa) – 8G12 (GPa) 4.55 3.8G13 (GPa) 4.55 2.8G23 (GPa) 5 2.8m12 0.07 0.1m13 0.07 0.25m23 0.4 0.25Ply strengthsXt (MPa) 621 414Xc (MPa) 760 458Yt (MPa) 594 414Yc (MPa) 707 458S12 (MPa) 125 105S23 (MPa) 125 65Intralaminar fracture toughness

Gtf (kJ/m2) 160 10

Gcf (kJ/m2) 25 1.562

Gtm (kJ/m2) 10 0.625

Gcm (kJ/m2) 2.25 0.14

Gs (kJ/m2) 2.25 0.14


4. Design of experiments

Design of experiments, or experimental design, is the design ofall information-gathering exercises where variation is present,whether under the full control of the experimenter or not. The pur-pose of it is to study the effect of some processes or intervention onsome objects. Design of experiment is a discipline which has broadapplications across all the natural and social sciences. A methodol-ogy for designing experiments was proposed by Ronald A. Fisher, inhis innovative book The Design of Experiments (1935).

Design of experiments is a very efficient statistical techniquewhich can be employed in various experimental investigations[3]. The design of experiments provides the capability to under-stand the design effects of various factors and their statistical sig-nificance as well [25]. The design of experiments is useful at thestage of data collection as it provides a systematic and rigorous ap-proach which generates valid, defensible and supportable datasets.

In the previous study by the authors, the sensitivity analysischaracterized four variables namely the thickness of the singlelayer, number of layers, stacking sequence and the material typeto be of most significance considering the impact behavior. There-fore, here these four factors are considered in the DOE study andthe different levels studied are listed in the Tables 4 and 5 forthe CFRP and GFRP plates respectively. The DOE matrix is differentfor the two materials because the idea was to collect data of the ab-sorbed energy for both the materials from the complete failure ofthe plates to the just slight damage or minimal damage to theplate.

In total, 216 experiments were conducted numerically with dif-ferent variations of the above mentioned factors with 108 each forboth types of fiber materials. The material properties of the carbon/epoxy and the glass/epoxy system are listed in Table 6. The resultswere calculated in terms of the absorbed energy with the impactenergy fixed at 27.55 J. The impactor dimensions, weight andvelocity are being kept constant in all the cases. The boundary con-

Table 4DOE table for CFRP plates.

Thickness Number of layers Stacking sequence

Factors Levels Factors Levels Factors Levels

0.12 1 16 1 [0/30/60/90] 10.14 2 20 2 [45/�45/0/90] 20.16 3 24 3 [45/30/�30/�45] 30.18 4 28 4 [60/45/�45/�60] 40.2 5 32 50.25 6 36 60.3 70.35 80.4 9

ditions are also kept the same throughout all the experiments. Thesimulations were performed in ABAQUS Explicit environment.

5. Neural network

Artificial Neural Network (ANN) or sometimes called neuralnetwork is an interconnected group of artificial neurons that usesa mathematical model or computational model for informationprocessing based on a connectionist approach to computation. Itis an adaptive system whose structure is modifiable based on theexternal or internal information that flows through the network.The name is given because of its ability to learn like human brainby examples. This technique is useful in pattern recognition, modelfitting or data classification. Once trained; ANN can be used to pre-dict the outcome of new independent data different from the train-ing set. The ability of ANN model to learn by example highly non-linear and noisy data is useful in our approach where we are deal-ing with statistical data. This feature is very useful in our problemwhere a mathematical relationship of the factors considered bysensitivity analysis with the absorbed impact energy is not avail-able but with the help of FEA simulations a lot of training data isavailable to us.

A neural network is a set of connected neurons, these neuronsreceive impulses from either input cells or other neurons and applya function and transmit the output to other neurons or the finaloutput cells. The neural networks can be multi-layered in whichcase one layer receives information from the preceding layer ofneurons and passes the output to the subsequent layers.

Fig. 7. A single neuron.


A neuron is a real function of the input vector (y1, y2 , . . . , yk).The training function for the neurons, available with MATLAB aretan-sigmoid, pure linear and log-sigmoid. For the training of inputneurons, tangent sigmoid (tansig) is used which is given as

f ðxÞ ¼ 2ð1þ e�2xÞ � 1

This function is equivalent to tangent-hyperbolic functiontanh(x) available in MATLAB but is usually faster. For the neuronsproviding connections to the output layer, a pure linear transferfunction is used.

Fig. 8. A multi-layered feed forward neural network.

Fig. 9. General configuration of artificial n

f ðxÞ ¼ x

The choice of output neurons depend upon the characteristic ofthe neural network, sigmoid output neurons are used for patternrecognition while linear output neurons are used for function fit-ting problems.

A graphical representation of a single neuron is shown in Fig. 7.A single neuron with ‘n’ number of inputs each represented by

‘x’ is a weighted sum of all the inputs and the bias, given as:

ai ¼ fX

n

Winxn þ b

!

5.1. Feed forward networks

A feed forward network works in the forward direction i.e. theflow of information is in only one direction along the connectionsfrom the input layer through the hidden layers of neurons to thefinal output layer. There is no feedback loop in these networksand hence the output does not affect the performance of the previ-ous layers or the same layer (see Figs. 8 and 9).

5.2. Learning method for the ANN

Learning is the major part of the neural networks training; thereare different methods for this purpose. The aim is to update theweight parameters at the interconnection level of the neurons.The most commonly employed learning algorithms are the super-vised learning, unsupervised learning and the reinforced learningalgorithms. For the purpose of prediction model for compositeplates, supervised learning algorithm was used in this study.

The supervised learning is the training of the network usingexamples. A predefined set of inputs are provided to the network

eural network for composite plates.


for which the output is already known. The network is trained iter-atively to reduce the error between the outputs of the networkwith the target output. A number of learning algorithms are avail-able; the most commonly used among them is the Back Propaga-tion Learning (BPL) algorithm. The algorithm used is known asthe Levenberg–Marquardt algorithm and is available with theMATLAB software.

5.2.1. Error estimationLet’s assume that the inputs are represented by x(1), x(2) and

x(3) and y denotes the desired output vector. The training of thenetwork is carried out in an iterative procedure where the error be-tween the target results and the output vector are measured usingthe Root Mean Squared Error. The error can be calculated using themean squared error,

MSE ¼ 1n

Xn

i¼1

ðyi � yiÞ2

where yi represents the target output and the yi represents the out-put vector. To calculate the root mean square we take a square rootof the MSE

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

Xn

i¼1

ðyi � yiÞ2

vuut

Fig. 10. Comparison of ANN accuracy of different size of data sets for training withthe response from ABAQUS simulations.

Table 7Testing ANN for 21 neurons for CFRP plates.

Input1 (thickness) mm Input2 (number of layers) Input3 (stacking sequence)

0.3 20 10.25 16 10.25 20 30.35 28 10.16 16 30.3 16 10.25 20 10.18 16 10.25 28 10.18 16 40.4 28 30.4 32 10.2 24 40.25 20 2

The optimization algorithm of differential evolution was used tofind the best ANN model, an objective function was defined whichcomputes the maximum error from one ANN model at a timewhich was based on a number.

Two separate ANN models were generated for the carbon/epoxyand the glass/epoxy plates. In total we had 108 different simulationdata for each type of material. Data set available for training ANNin this study is 108 samples, few iterations of ANN models weretried coupled with a differential evolution algorithm for the opti-mization of the ANN model in terms of the number of neuronsand the hidden layers. The data set was randomly distributed inthree sets, for the training, testing and validation of the model.The training was carried out by randomly selecting 94 data pointsand the rest were divided equally for the testing and validation.

6. Differential evolution algorithm

The optimization algorithm of differential evolution was used tofind the best ANN model, an objective function was defined whichcomputes the maximum error from one ANN model at a timewhich was based on the number of neurons. This optimization ofthe ANN model was necessary to find the best possible configura-tion of ANN models which depend upon the number of hidden lay-ers and neurons. The ANN model configuration thus obtained wasthen train to predict the amount of absorbed energy for the com-posite plates. Two separate models were used to predict the behav-ior of composite plates based on carbon or glass fibers.

The optimization algorithm works on an initial populationwhich contains the number of neurons and number of hidden lay-ers in one network, among a population of candidate networks ittrains and estimates the RMSE for each and compare for the bestnetwork, i.e., one with the least RMSE value. The important factorsin the consideration of DE are the initial population size, limits ofthe genes and the cross over ratio. For the purpose of this study,an initial population size of 200 individuals were generated withnumber of neurons limit as [6, 100] and number of hidden layers[1,2]. The cross over ratio was selected to be 0.8 and the numberof generations was 100.

7. Results and discussions

The carbon/epoxy composite plates’ impact behavior was welldefined compared to the glass/epoxy composite plates. It is notedthat the more the data follows a recognizable pattern, the betterthe correlation will be, as the ANN model described earlier usesthe target response to calculate the weights of each neurons. Themodel for carbon/epoxy plates needed only 21 neurons and a sin-gle hidden layer containing all the neurons. The model is generally

Actual response (ABAQUS) J Simulated response (ANN) J Difference

5.9155 6.105 �0.18956.7855 6.8955 �0.115.7807 5.6217 0.1592.7507 2.5044 0.24637.5475 7.3142 0.23336.5986 6.4669 0.13177.074 7.0582 0.01587.7121 8.0439 �0.33185.7693 5.7452 0.02417.1083 7.08 0.02831.2529 1.3213 �0.06840.2346 0.0313 0.20334.631 4.7639 �0.13295.3035 5.3961 �0.0926


supposed to predict the behavior accurately when the absolute er-ror between the predicted and the targeted values is at least twoorders less in magnitude.

The efficiency of training the neural network depends upon therandomness of the training data set, to achieve this a random num-ber generator was used in MATLAB programing which distributesrandom data points for the training, testing and validation pur-poses. Another factor which is important for the purpose of train-ing is the size of the training set; MATLAB uses by default 15% ofthe data for testing and 15% for the validation phases. Since, thedata set available was limited it was reduced to about 6% eachfor testing and validation. Therefore, the data set available for

Fig. 11. Correlation between the predicted and the target response for CFRP plates.

Fig. 12. Actual response and the predicted response for CFRP plates.

Table 8Independent test cases to verify ANN model.

Input1 (thickness) mm Input2 (number of layers) Input3 (stacking sequence) Actual response (ABAQUS) J Simulated response (ANN) J Difference

0.24 24 1 5.9006 5.9836 �0.0830.16 30 4 4.6322 5.0069 �0.37470.22 26 2 4.6903 4.9347 �0.24440.14 18 3 7.7589 8.5684 �0.80950.36 32 2 0.5093 0.6132 �0.1039

Fig. 13. Absorbed impact energy prediction using ANN model for different layerthickness.

Fig. 14. Absorbed impact energy prediction using ANN model for different numberof layers.

Fig. 15. Correlation between the predicted and the target response for GFRP plates.


training was about 94 and 7 each for validation and testing. Fig. 10demonstrates the fact that the dependence on the size of dataavailable for training is crucial. It is not a lot different for most ofthe instances but the most accurate network is the one whereabout 87.5% of data set was available for training. Therefore, it isalways important to have as big a data set possible for the trainingto increase the accuracy for the future prediction purposes. Since,the initial data set consisted of only 108 simulations, a further fivesimulations were performed and the results from ANN were simu-lated to confirm the accuracy.

The ANN model for carbon/epoxy system has a root meansquare error of just 0.18 J with the maximum error of 0.6652 J.

A separate verification was carried out with simulations fromABAQUS and the ANN model for the cases presented in Table 7.The verification gives the further confidence in the ANN modeland its use in generating the population for the optimization pro-

Fig. 16. Actual response and the predicted response for GFRP plates.

Table 9Testing ANN for 24 neurons for GFRP plates.


0.6 28 10.25 32 30.4 28 30.25 32 10.45 36 40.35 36 30.4 36 10.4 28 20.35 32 40.45 32 30.5 36 20.3 24 10.25 36 40.35 24 4

Table 10Independent test cases to verify ANN model for GFRP plates.


0.26 24 20.42 30 40.35 26 10.54 34 20.36 36 3

cess. Fig. 11 shows the correlation between the target and the pre-dicted response while Fig. 12 represents the difference betweenthe actual and the predicted response. Table 8 presents the pre-dicted absorbed energy in the carbon/epoxy composite platesbased on the inputs not considered in the training set.

ANN models here are used for the purpose of prediction of theresponse of different configurations of composite plates underthe impact loads. The loading conditions and boundary conditionsare kept the same for all the cases. The ANN models provide advan-tages in situation where the amount of absorbed energy has to becalculated but the usual simulations in ABAQUS is time consuming.Properly trained ANN models in this case of carbon/epoxy platesare able to predict within a certain accuracy range and as evidentfrom the tables provided above are within a range of ±1 J whichis acceptable. The error is generally high towards the cases wherethe damage is more; in cases where the plate is able to rebound thestriker with minimum energy absorbed the error in the predictionfrom the ANN model is about ±0.3 J. Figs. 13 and 14 represents theusefulness of the ANN model in pattern recognition and the predic-tion of the function with respect to the variation in layer thicknessand number of layers respectively. The number of data samplesused for training was small as compared to the ability to predictfor a variety of different inputs.

Similarly, ANN model was trained to predict the amount of ab-sorbed impact energy by the glass/epoxy composite plates underthe same loading conditions. The ANN model for glass fiber platesuses 24 neurons in a single layer and is able to predict the amountof absorbed energy with maximum error of 1.1047 J and root meansquare error of 0.33 J.

Fig. 15 represents the correlation between the actual and thesimulated response from the ANN model while Fig. 16 demon-strates the accuracy in the prediction of the absorbed impact en-ergy by the ANN model superimposing the results from ABAQUS.Table 9 gives the results used for the testing of the final trainedANN model. An independent data set was used to predict the re-sponse from the ANN model for glass/epoxy plates and is presentedin Table 10.

The number of data samples for training is the same for carbonand glass fiber plates but the error is more pronounced for the glass


1.6022 1.6531 �0.050914.8979 14.9839 �0.08611.1732 11.0837 0.089513.8011 12.9575 0.8436

2.5115 2.4935 0.0188.6502 8.2851 0.36518.5923 8.8273 �0.235

14.9456 14.0875 0.85815.187 5.7195 �0.53258.2871 8.5516 �0.26450.7561 0.7411 0.015

12.686 12.8399 �0.15396.3016 5.7934 0.5082

11.046 11.6601 �0.6141


13.37359 15.5417 2.16816.14928 6.2809 0.1316

12.69973 13.153 0.45320.602984 0.6865 0.08358.449098 8.3282 �0.1209


fiber plates due to the reason that the data for the response is notfollowing a pattern which makes it harder to model ANN. This er-ror can be reduced by introducing more data for training purposes.

The correlation data shows that the neural network with 21neurons is significantly better than the other networks that weretried for the composite plates. There is a 99.91% correlation withthe target data of training which is very high accuracy for the CFRPplates. The correlation between the target data and the ANN modelis about 99.94% for the training set in the GFRP plates but the cor-relation for the testing and validation cases is lower but still withinthe acceptable range of 96%.

8. Conclusion

This paper presented the ANN models for prediction of theamount of absorbed energy. We have discussed in this study theefficiency and usefulness of the neural networks in the ability tofit functions and predict the amount of absorbed energy with verylittle error. The main conclusions from this chapter can be summa-rized as:

ANN models are very strong and useful tools for the function fit-ting of non-linear behavior and as observed in the case of CFRPplates are able to predict the absorbed energy with very littleerror.The accuracy of the ANN models depend upon the behavior ofthe training data sets, if there are too much sudden variationsin the training data as was observed in the results from thecomposite pipes then the model can be prone to errors.A better way to model ANN with training data as in our case isto simulate and generate a very big training data. In our study,we had around 100 data each for the flat plates. As a rule ofthumb, it is suggested that the data size should be in the rangeof 500–1000 for a very accurate model.This paper presented an approach which can be used towardsthe optimization of impact performance of the composite platesusing DOE with the FEM techniques to simulate the experi-ments and the approximation of the analysis results usingANN model.The DOE method is very useful in acquiring the full data varia-tions and their effects on the output results.The ANN model fitting technique was used for model fitting andcan be used to approximate and predicts the behavior of com-posite plates under impact loads.A number of ANN models were tried and after trying with var-ious iterations, a model with 21 neurons was selected based onthe least RMSE value for the CFRP plates and a model with 24neurons was selected for the GFRP plates. The ANN model willbe subsequently used with optimization algorithm to find anoptimized configuration with respect to the cost.

Acknowledgements

The authors thankfully acknowledge the support provided bythe King Fahd University of Petroleum and Minerals, Dhahran, Sau-di Arabia for conducting this research.

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