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Wear 268 (2010) 708–714

Contents lists available at ScienceDirect

Wear

journa l homepage: www.e lsev ier .com/ locate /wear

odeling the sliding wear and friction properties of polyphenyleneulfide composites using artificial neural networks

ada A. Gyurovaa,∗, Paz Minino-Justelb, Alois K. Schlarbc

Institut fuer Verbundwerkstoffe GmbH, University of Kaiserslautern, Erwin Schroedinger Str. 58, 67663 Kaiserslautern, GermanyHigher Technical School of Industrial Engineering, Campus Lagoas-Marcosende, 36310 Vigo (Pontevedra), SpainChair of Composite Engineering, University of Kaiserslautern, Gottlieb Daimler Str. 44, 67663 Kaiserslautern, Germany

r t i c l e i n f o

rticle history:eceived 11 March 2009eceived in revised form0 November 2009ccepted 16 November 2009vailable online 3 December 2009

a b s t r a c t

In the present study artificial neural network (ANN) approach was used for the prediction of wear andfriction properties of polyphenylene sulfide (PPS) composites. Within an importance analysis the rele-vance of characteristic mechanical and thermo-mechanical input variables was assessed in predictingthe response variable (specific wear rate and coefficient of friction). The latter is believed to be of help fora better understanding of the wear process with these materials. An optimal brain surgeon (OBS) methodwas applied to prune the ANN architecture by identifying and removing irrelevant nodes in its structure.

eywords:olymer compositesear

rictionrtificial neural networkruning

The goal was minimizing the training computational cost and improving prediction. Finally, the opti-mized ANN was utilized to gain knowledge for the tribological properties of new material combinations,which were not tested. The quality of prediction was good when comparing the predicted and real testvalues.

© 2009 Elsevier B.V. All rights reserved.

ptimal brain surgeon algorithm

. Introduction

Wear and friction originate from multiple sets of complexnteractions on microscopic scale between surfaces that are in

echanical contact and slide against each other. These interactionsepend on the materials, geometrical and topological characteris-ics of the surfaces and overall conditions under which the surfacesre made to slide against each other, e.g. loading, temperature,tmosphere, type of contact, etc. [1]. In the simulation of wearnd friction tests known or estimated properties of the mate-ial are input to the model, and the expected responses of theirtual tool to such variables as load cycles, deflections, temper-ture excursions, etc. are calculated. The principle benefit of neuraletwork modeling compared to other approaches is in its capa-ility for accurate predictions when significant non-linearity andysteresis are present simultaneously. The latter is not easy tottain with conventional curve fits. Furthermore, the neural net-

orks will readily handle irregular or random inputs [2]. Based

n the aforesaid, artificial neural network (ANN) approach seemso have good potential to save time and cut expenses in solvingarious friction and wear problems. A preliminary investigation

∗ Corresponding author. Tel.: +49 631 2017238; fax: +49 631 2017196.E-mail address: lada.gyurova@ivw.uni-kl.de (L.A. Gyurova).

043-1648/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.wear.2009.11.008

of neural networks techniques to predict tribological propertieswas done by Jones et al. [3] on metals. Some other works inthe field of ANNs for wear prediction include: Umeda et al. [4],who characterized wear particles and their relation to the slid-ing conditions; Myshkin et al. [5], who classified wear debris byapplying an ANN approach; Lin and Lin [6], who used it for toolwear monitoring in face milling; Subrahmanyam and Sujatha [7],who preformed ANN-studies for the diagnosis of localized defectsin ball bearings; and Das et al. [8], who evaluated wear of turn-ing carbide inserts. With reference to polymer composites, Veltenet al. [9] were the pioneers in exploring the application of ANNto these materials and used an ANN to predict the wear volumeof short-fiber/particle reinforced thermoplastics. However, at thisearly stage of research with ANN applied to wear prediction of poly-mer composites, the ANN model gave only reasonable accuracy andthere was still room for improvement. Subsequently, in a seriesof methodological studies [10–19] ANN approach was applied for:(1) pattern completion for friction and wear properties of polymercomposites provided that only a portion of an input pattern is avail-able (2) parameter studies related to external testing conditions

and (3) indicator of the importance of various input characteris-tic properties for the friction coefficient and wear rate of polymercomposites. A well-trained ANN tool is expected to be helpful notonly for designing new materials, but also for further understand-ing of the modeled nonlinear relations. In all the cases the ANN

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rediction profiles showed good agreement with the measuredesults.

In the present work artificial neural network approach waspplied for studying sliding wear and friction of polyphenyleneulfide (PPS) composites. A systematic parameter study was car-ied out using ANN in order to elucidate which mechanical andhermo-mechanical properties exhibit stronger correlation to theribological properties. Optimal brain surgeon (OBS) algorithm, anffective technique for network optimization, was used to improvehe performance and efficiency of the ANN. Subsequently, the opti-

ized ANN was applied to predict the wear properties of PPSomposites. The selected input parameters were filler and matrixolume fractions along with the testing conditions. Finally, by seek-ng the lowest area on the predicted 3D profile of specific wear rate,he best material composition could have been found.

. Artificial neural network approach

ANNs operate in the same way as the brain’s neural networkFig. 1a) and use interconnected nodes (called neurons) to transfernformation. ANN structure is divided into three segments: inputayer, hidden layer, and output layer (Fig. 1b). The number of neu-ons in the input and output layer is fixed to be equal to that of

nput and output variables, respectively, whereas the hidden layeran contain more than one layer, and in each layer the numberf neurons is flexible. In the hidden layers as well as in the out-ut layer, the individual neuron acquires the information from theeurons in the former layer, and transforms the information via a

Fig. 1. Schematic representation of (a) biological and (b) artificial neural network.

Fig. 2. Schematic illustration of ANN project cycle.

transfer function with weights and bias, prior to output the result[20–24].

The structure of ANN can be expressed as:

Nin − [N1 − N2 − . . . − Nh]h − Nout (1)

where Nin and Nout represent the number of input and output vari-ables, respectively. N1, N2, and Nh are the numbers of the neuronsin each hidden layer. The number of hidden layers is denoted bysubscript h.

To imitate a real neuron, each input is weighted with a fractionbetween 0 and 1. The weight specifies how significant the incomingsignal for that input will be. All of the incoming signals’ weights aresummed together and the total equals the net value of the neuron.Each artificial neuron is also set a number that corresponds to thethreshold or point over which the artificial neuron will shoot andtransfer the signal to another neuron. If the net value is greaterthan the threshold, the neuron will shoot. If the value is less thanthe threshold, it will not shoot. The output from the shooting isthen transferred to other neurons that are also weighted. In otherwords, the learned knowledge generalized in the training processis memorized in terms of the state of these weights. Additionally,a bias component which is always put to 1 and which connects toall components except those in the input layer is placed. Its task isto pull the inputs to the hidden and outputs into the correct rangefor the squashing function [20–24].

Training is the act of continuously adjusting the connectionweights until they reach distinctive values that allow the networkto produce outputs being close enough to the actual desired out-puts. The accuracy of the developed model, therefore, depends onthese weights. Once optimum weights are reached, the weights andbiased values encode the network’s state of knowledge [25]. Theevaluation of the network performance is done in terms of a meanrelative error, which provides comparison between predicted val-ues for different network parameters and desired values. The meanrelative error (MRE) is calculated as follows:

MRE = 1n

n∑i=1

|di − Oi|di

(2)

where di is the desired value, Oi the predicted output value andn the number of data. The lower the MRE, the better the networkperformance is [20,25].

The neural network project life cycle can be summarized as fol-lows (Fig. 2). In most cases the goal is to create ANN solution capableof generalizing on examples, on which it was not trained, whilemaintaining an optimal level of accuracy for those on which it was.

In the usage of artificial neural network an essential draw-

back might be the complexity of the network, which is directlyrelated to problems such as poor generalization as well as overfit-ting (i.e. the network only memorizes the data for training, but doesnot generalize correct knowledge). In other words, the initial net-work architecture supplies numerous interconnections between

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Fig. 3. Schematic representation of pruning.

he neurons, some of which are not decisive for its performance.y eliminating these non-useful redundant connections the ANNtructure might be simplified (Fig. 3) leading to improved gener-lization capability of the network, accordingly better prediction26,27].

To know which weights should be eliminated is a difficult issue.here exist diverse approaches (or pruning algorithms) to optimizehe network architecture, which are based on different criteria. OBSlgorithm follows the criterion of minimal increase in error on theraining data [28]. The single steps constituting the OBS optimiza-ion procedure can be summarized as follows:

- Training a reasonably large network to minimum error.- Estimating the Hessian matrix of the second-order derivatives of

the training error criterion with respect to the existing weights.- Evaluating the “saliency” of every weight, i.e. the increase in the

training error resulting from the elimination of the weight.- Deleting the weight with the smallest saliency and updating the

remaining weights.

. Experimental

.1. Materials, processing and testing

In the present paper Fortron PPS grade 0214 (Ticona GmbH)as selected as a matrix material. The following additives were

hosen to enhance the matrix wear resistance: short carbon fiberKureha M-2007S, Kureha Chemicals GmbH), graphite (Superior039, Superior Graphite Europe Ltd.), PTFE (Dyneon 9207, Dyneon),ub-micro TiO2 (Kronos 2310, Kronos Titan GmbH) with an aver-ge diameter of 300 nm. The compounding of the fillers with theatrix was achieved via twin-screw extrusion. The total content of

he fillers in the matrix was up to 35 vol.%. The extrudates wereubsequently injection molded to rectangular plates. To ensuredentical flow conditions the test specimens were machined onlyrom the middle section of the molded plates. Based on its sim-licity and flexibility in terms of test conditions and specimenhape, the pin-on-disk test configuration was chosen for evalu-tion of the friction and sliding wear behavior of the materials.he testing conditions (pressure (p) and sliding speed (v)) werearied in the pv-range from 1 MPa m/s to 9 MPa m/s. At leasthree pins were tested per each testing condition. The surfaceoughness of the counterpart (LS 2542, INA Scheffler KG) waseasured as average roughness Ra = 0.19 �m by a Mahr Perthome-

er (Perthen, Mahr-Perthen). The testing time was fixed to 20 h,llowing the system to reach steady-state tribological conditions.

or some of the materials, e.g. pristine PPS, the test was stoppedfter 1 h due to the excessive wear. In the course of the exper-ments both the normal and frictional forces were recorded toetermine the friction coefficient. The specific wear rate, ws, wasalculated from the mass loss of the specimen after the testccording to:

68 (2010) 708–714

ws = �m

�vtFN

(mm3

Nm

)(3)

in which �m is the mass loss, � is the density of the material, v isthe sliding speed, and t is the duration of test. FN represents thenormal force imposed on the specimen during sliding.

3.2. ANN datasets, architecture, training and optimization

Two datasets were used in this work. The one for the specificwear rate (database I) contained 95 independent data measure-ments and the other one for the coefficient of friction (databaseII) contained 90 independent data measurements. Both datasetsincluded the material compositions (volume fraction of matrix,fillers, reinforcing agents and lubricants), the testing conditions(pressure and sliding speed) as well as some characteristic mechan-ical and thermo-mechanical properties of the PPS composites (e.g.tensile and compressive properties tested at room temperaturealong with DMTA properties determined in the range 23–230 ◦C)as input parameters; the output parameters were the tribologicalproperties (specific wear rate and friction coefficient). In addi-tion, the input variables in these databases were classified asprimary (material compositions and testing conditions) and sec-ondary (mechanical and thermo-mechanical properties). 80% of thedata in each dataset was used for training; the remaining 20% of thedataset was utilized for testing. The training and testing processeswere repeated for 200 times. The maximum number of iterations(epochs) in the training process was 1000. The training processstopped when either the value of end iteration was reached or theMRE minimum was attained. Based on earlier research activitiesin our group the learning method selected was traingdx (gdx). Thestructure of the hidden layer is a very sensitive question in the ANNperformance [11]. In this work the selected configuration for train-ing and prediction for the specific wear rate was 7 − [9 − 3]2 − 1and the one for the coefficient of friction was 7 − [3 − 1]2 − 1 inaccordance with previously done methodology studies [13].

The graphical user interface (GUI) utilized for performing train-ing and prediction with the ANN was created at IVW GmbHbased on MATLAB 7.0.4 environment. This GUI allows the userto select the number of hidden layers and hidden layer nodes(neurons), iterations used during the model training, learning algo-rithm, learning rate and transfer functions. The computer usedfor performing training and prediction was PC Pentium (R) 4 CPU2.00 GHz. For ANN optimization (calculation of saliencies), JavaNeural Network Simulator (JavaNNS), Version 1.1, developed atthe Wilhelm-Schickard-Institute for Computer Science in Tübin-gen (Germany), was used [29]. Detailed information on the createdGUI as well as ANN optimization can be found in [30].

4. Results and discussion

4.1. Importance analysis

In the past the correlations between wear resistance and char-acteristic properties of polymers have already been interpretedin terms of various semi-empirical equations. To mention few:Ratner–Lancaster equation [17,31,32] involved the relationship ofthe single pass abrasion rate with the reciprocal of the product ofultimate tensile stress and strain; Friedrich and co-workers [17,33]tried to link the erosive wear rate of polymers with the quotientof their hardness to fracture energy. Based on these equations it

was possible to approximate the wear behavior of polymers undercertain circumstances. Still, the wear phenomenon is very com-plex and depends on numerous mechanical as well as a range ofadditional factors. In other words, simple functions cannot alwaysaccount for all the prevailing mechanisms in the process of wear.

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ecently, a novel solution (ANN) has been proposed in the com-unity [9,14,17] for trying to better understand the mechanism

f wear and analyze the importance of characteristic propertiese.g. modulus, strength and failure strain) for the wear rate andriction coefficient of polymer composites. Moreover, such char-cteristic properties are in the normal case easier to obtain thanhe complex tribological ones. Consequently, the success of predic-ion could be of benefit to reduce the number of tribo-experiments.y now, it has been demonstrated that material compositions andesting conditions are essential to obtain reasonable predictedesults [10–14,17,34]. Still, properly selected input parametersight assist to reach a satisfied predictive quality even with a

elatively small training dataset [18,34–36]. For instance the com-arison of the two examples of fatigue life prediction [34–36],howed that the use of fiber orientation as input data yielded quitehigh predictive quality with a training set of only 92 data, taken

rom unidirectional composites [36], and the result was even bet-er than the one achieved in [35] with more than 400 data, takenrom laminates. In a preliminary work of Friedrich and Zhang [17]t was established that some secondary parameters exert greatnfluence on the prediction quality. In this respect, it was the goalf this work to investigate the effect of the so-called secondaryarameters (Section 3.2), on sliding wear and friction. Choosing theecondary parameters as input (along with the primary ones, whichre referred to as “base”) allowed us to rank them according to therediction quality. The latter was evaluated by the MRE of the ANNutput values related to the real measured data of the test dataset.

It has already been established by Zhang et al. [17] in an ANNmportance analysis study that the yield stress exhibits a strongependence to erosive wear of thermoplastic polymer (polyethy-

ene (PE)) compared to other properties such as Young’s modulus,rystallinity, yield strain or fracture energy. This trend was alsoxperimentally confirmed in an earlier publication of Friedrichnd co-workers [17,33]. For sliding wear, it has been found in theresent investigation (Fig. 4) that a combination of tensile mod-lus and strain represents the strongest correlation with wearerformance (MRE ≤ 0.68). A similar effect was also experimentallyscertained for the same PPS-systems by Gyurova et al. [37] as wells by Tsukizoe and Ohmae for fiber reinforced plastics [38].

The amount of wear of a material due to contact pressure and

elative motion of a solid counterpart is based largely on diversedhesive and abrasive wear mechanisms [39,40]. From microscopicbservations of polymer matrix surfaces worn by steel counterpartst has been established that the major contributions to wear areaused by a series of plastic deformation and rupture in a thin sur-

Fig. 4. Ranking of importance of input variables to

68 (2010) 708–714 711

face layer, plowing a larger material volume and subsequent cuttingof plastically deformed areas [40]. The mathematical description ofsuch behavior should follow the correlation that the wear volumeis inversely proportional to the hardness of the wearing mate-rial (resistance of the material against indentation of counterpartasperities) [39,40]. In addition, the wear volume depends throughthe wear coefficient and the geometry of the surface morphology,on two kinds of material physical properties: the surface energywhich is associated with adhesion and frictional forces (given bythe friction coefficient) and those properties of the material thatare responsible for the mechanisms by which material is detachedfrom the surface. These are basically mechanical properties suchas ultimate tensile strength and elongation to fracture [40]. More-over, higher stiffness lessens the real contact surface yielding loweradhesion, hence lower wear [41]. Likewise, it was observed thatthere exist almost linear relationship between the wear volumeand the reciprocal of the ultimate elongation at break [42]. All thisexplains the predicted strong correlation of the tensile propertiesto wear performance.

Microhardness as well as damping properties (storage modu-lus, mechanical loss factor) maintains the second place (Fig. 4). Thissuggests that damping behavior may be key aspect in the slidingwear process. Such tendency has previously been observed for theerosive wear of polyurethane (PUR) [17]. Nevertheless, the glasstransition temperature data in combination with storage modulusand mechanical loss factor as input reduces this strong correla-tion to sliding wear performance of the last two parameters. As tothe microhardness results, most tribological cases involve condi-tions where a hard body indents, impinges or slides against anothersofter surface. Therefore, the hardness, work hardening ability andstrain to fracture of each material involved in the mechanical inter-action are crucial parameters which control the extent and depthto which strain builds up below each surface prior to microfrac-ture and wear loss. Furthermore, the magnitude of the stresses aswell as the rate at which strain energy is conveyed and dissipatedbetween two bodies during their interaction, also determines therespective levels of subsurface strain build up and fracture [43]. Thecompressive properties as well as notch Charpy impact strengthshowed relatively weak influence on sliding wear of PPS compos-ites, except for the compressive strength. The results for the notch

Charpy impact strength conformed well to an earlier experimentalinvestigation on PPS composites by Gyurova et al. [37]. The impor-tance of compressive strength for the wear behavior is attributedto the fact that during sliding the material is in general subjectedto compressive loading.

specific wear rate of PPS composites by ANN.

712 L.A. Gyurova et al. / Wear 268 (2010) 708–714

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amount of graphite and SCF the specific wear rate of the com-posites became the lowest in the range 2–8 vol.% nano-particulatefiller. In the present study according to the ANN prediction the bestwear resistance could be achieved by the PPS composition with3 vol.% TiO2 and 10 vol.% SCF. For comparison, in a previous study

Fig. 5. Ranking of importance of input variabl

The predictive quality results for the coefficient of friction arehown in Fig. 5. It can be seen that similar to wear rate micro-ardness, tensile strength or strain as well as the combination ofll the three tensile properties, the compressive modulus and espe-ially the storage modulus improved the quality of prediction whenompared to the reference case. Nevertheless, the strength of thismprovement was not as pronounced as for the specific wear rate.imilar to other studies [13,34,44] the predictive quality hereinhowed very profound dependence on material composition andv-data. For all the other parameters (compressive strength andtrain, notch Charpy impact strength, etc.) no strong correlationould have been established to the sliding friction of PPS compos-tes.

As it can be seen in Fig. 5 the reference value of MRE for slidingriction was lower than for the specific wear rate (Fig. 4). The lat-er conforms well to the already established results by Jiang et al.10,12] and Zhu et al. [18], who demonstrated that a certain amountf training data is a vital prerequisite for a neural network to exportrediction results of high accuracy.

.2. Optimization and prediction with ANN

The “black box” status of ANNs has made some research commu-ities unconvinced for at least two reasons. To begin with, even formodest number of inputs (independent variables) and nodes, theumber of interconnections and, consequently, adjustable weightsurns out to be quite vast. Secondly, too much adjustable param-ters might lead to data overfitting — the network no longereneralizing the data but fitting also its noisy peculiarities [45].n this respect, research activities are directed to the applicationf so-called “weight elimination” or “pruning” techniques, whichim to generate a network with as small number of weights asossible (i.e. neither under- nor overfitting of the data can takelace). The pruning process involves the following steps: first taken existing network, which satisfactorily fits the data and subse-uently remove connections, even whole nodes with their pendantonnections, without sacrificing the fitting capabilities of theetwork.

The architecture of the ANN prior to pruning and after pruning

s showed in Fig. 6(a)–(b). As expected the number of hidden nodesfter pruning has been strongly decreased from 9 to 2 in the firstnd from 3 to 2 in the second hidden layer. It will be seen below thatruning the network permits to obtain better prediction capabilityia the simplified network architecture.

riction coefficient of PPS composites by ANN.

The prediction performance of the network before and afterpruning is compared in Fig. 7 and Fig. 8 below. It can be seenthat in both cases the prediction fits reasonably well the experi-mentally generated results. However, the prediction performanceof the pruned network is superior and seems to better catch theunderlying functional relationships for the investigated materials.Likewise, the pruned ANN gives more realistic conformity to resultspreviously established in the practice with other thermoplastic-and thermosetting-based materials under pv-product of 1 MPa m/s[46]. Zhang and Friedrich [46] also found out that with a constant

Fig. 6. ANN architecture: (a) initial and (b) pruned.

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ig. 7. ANN predicted 3D profiles of the specific wear rate (pv = 1 MPa m/s) withoutruning.

f Jiang et al. [13,44], using a smaller PPS-database (66 groups ofndependent tests) and a Powell–Beale conjugate gradient traininglgorithm, the best composition estimated by ANN was PPS with5 vol.% SCF and 6 vol.% TiO2. Further, a comparison of the predic-ion profile (Fig. 7) and the one generated in our earlier publication44] shows that the agreement between measured and predictedesults improved significantly with the expanded database for theame input and output parameters. The latter conforms well to for-erly established trend by Jiang et al. [10,12] and Zhu et al. [18]

oncerning the influence of the size of the training dataset on theNN prediction capabilities. Nevertheless, it should be also borne

n mind that with the expanded database a different training algo-ithm was applied, namely variable learning rate backpropagation

ig. 8. ANN predicted 3D profiles of the specific wear rate (pv = 1 MPa m/s) withruning.

68 (2010) 708–714 713

(gdx) algorithm, which seemed to better suit the present case andalso contributed for the enhancement in prediction capacity of theANN. In our former studies [10,12,13,44] the Powell–Beale conju-gate gradient (cgb) algorithm was selected because it yielded thehighest prediction accuracy among all the other studied algorithms(gradient descent with momentum (gdm), scaled conjugate gradi-ent (scg), BFGS quasi-Newton method (bfg), Levenberg–Marquardtalgorithm (lm)). Still, the variable learning rate backpropagation(gdx) algorithm was not evaluated in that early research [10,12].

Finally, the prediction (Fig. 8) demonstrates the excellent capa-bility of the optimized ANN to prefigure the reinforcing action ofgiven filler. For the particular case of SCF, it has become obviousby now that such reinforcement is crucial for enhancing the wearresistance of both neat PPS and sub-micro-filled PPS composites[13,37,44]. A fraction of 10–15 vol.% yields a 100 fold reductioncompared to the neat matrix. The latter is related to the improvedload carrying capacity of the composite by the fiber reinforcement.It is evident that a content of 10 vol.% SCF exhibits an optimumeffect for wear minimization. Further decrease in the specific wearrate can be observed with the addition of the particulate sub-micro phase. Zhang and co-workers [13,44,46] presumed that thismight be attributed to the so-called rolling effect with the particlesbetween the two mating surfaces that helps in the formation of athin, uniform, and tenacious transfer film, reduces the shear stressalong with the friction coefficient and contact temperature. Still,this rolling mechanism is until now only hypothetical. Additionalinvestigations should either prove it or reject it experimentally.

5. Conclusions

In the present work artificial neural network approach wasapplied for studying wear and friction properties of PPS composites.In order to investigate the relevance of potential input variablesin predicting the response variable (specific wear rate and coef-ficient of friction), MRE criterion was applied. The analysis of theinput significance showed that along with material compositionand testing conditions a combination of tensile modulus and strainrepresents the strongest correlation with wear performance. Thesecond place was maintained by microhardness and damping prop-erties. The compressive properties as well as the notch Charpyimpact strength showed relatively weak influence to sliding wearof PPS composites, except for compressive strength. The predic-tive quality results for the coefficient of friction were improvedwhen microhardness, tensile properties, compressive modulus andespecially storage modulus were used as input along with materialcomposition and pv-data. Still, the strength of this improvementwas not as marked as the one for the specific wear rate. Further,the values of MRE for sliding friction were much lower (0.1–0.12)than the ones for the specific wear rate (0.6–0.78). The latter con-forms well to previously established results and is an indication forthe necessity to expand the working database for the specific wearrate in order to increase the prediction accuracy.

OBS algorithm, an effective technique for network optimization,was used to improve the performance and efficiency of the artifi-cial neural network by removing the irrelevant networks nodes.Subsequently, the prediction performance of the network priorto and after pruning was compared. In both cases the predictionmatched reasonably well the experimentally generated results.Nevertheless, the prediction performance of the pruned networkwas superior and could better give a correct representation of theunderlying correlations, particularly, for low concentrations of SCF

and high volume fraction of TiO2. By seeking the lowest area on thepredicted 3D profile of the specific wear rate, the best material com-position could have been identified, namely PPS with 3 vol.% TiO2and 10 vol.% SCF. Finally, the prediction results demonstrated onceagain the excellent capability of the optimized ANN tool to envisage

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cknowledgement

The authors gratefully acknowledge the financial support ofhe German Research Foundation (DFG FR 675/45-1: Wear predic-ion of polymers and composites using an artificial neural networkpproach and DFG SCHL 280/7-2 “Vorhersage der Verschleißeigen-chaften von Polymeren und Verbundwerkstoffen mit Hilfe vonünstlichen neuronalen Netzen”). Ms. Minino-Justel would like tohank “Beca Faro Programme” for providing financial funding forhe realization of her diploma thesis at IVW GmbH.

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