International Journal of Polymer Science
Volume 2015 (2015), Article ID 315710, 11 pages
http://dx.doi.org/10.1155/2015/315710

Research Article

Application of a Neural Network Model for Prediction of Wear Properties of Ultrahigh Molecular Weight Polyethylene Composites

Halil Ibrahim Kurt and Murat Oduncuoglu

Technical Sciences, University of Gaziantep, 27310 Gaziantep, Turkey

Received 7 December 2014; Revised 25 May 2015; Accepted 31 May 2015

Academic Editor: Togay Ozbakkaloglu

Copyright © 2015 Halil Ibrahim Kurt and Murat Oduncuoglu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

In the current study, the effect of applied load, sliding speed, and type and weight percentages of reinforcements on the wear properties of ultrahigh molecular weight polyethylene (UHMWPE) was theoretically studied. The extensive experimental results were taken from literature and modeled with artificial neural network (ANN). The feed forward (FF) back-propagation (BP) neural network (NN) was used to predict the dry sliding wear behavior of UHMWPE composites. Eleven input vectors were used in the construction of the proposed NN. The carbon nanotube (CNT), carbon fiber (CF), graphene oxide (GO), and wollastonite additives are the main input parameters and the volume loss is the output parameter for the developed NN. It was observed that the sliding speed and applied load have a stronger effect on the volume loss of UHMWPE composites in comparison to other input parameters. The proper condition for achieving the desired wear behaviors of UHMWPE by tailoring the weight percentage and reinforcement particle size and composition was presented. The proposed NN model and the derived explicit form of mathematical formulation show good agreement with test results and can be used to predict the volume loss of UHMWPE composites.

1. Introduction

Polymers have high elasticity, good process ability, and reasonable strength, so they can be called multifunctional materials. Polymer-based composites are widely used in various applications and many fields, including microelectronics, biomedical engineering, electrical devices, and filtration [1–5]. Polymer-based nanocomposites formed by adding a small amount of micro- and nanoparticles to the matrix have created great interest in engineering and science. Composites with nanoparticles display superior thermal, electrical, and mechanical properties [6–8]. The properties of the materials have been improved by adding fillers such as graphite nanosheets, CNTs, and boron nitride (BN) to polymer matrices [9–11].

UHMWPE is widely used as the matrix material in the production of polymer matrix nanocomposites. UHMWPE has so many excellent properties such as being light in weight, corrosion resistant, biocompatible, and self-lubricant. Due to these special properties and several advantages, it has gained worldwide acceptance and is widely used in military, industrial, medical, and consumer applications involving wear and friction [12, 13]. UHMWPE is a complicated material, meaning that several factors can be responsible for wear. One method of increasing the wear resistance of UHMWPE is the adding of fiber fillers and nano- and microparticles in the composition and they are called UHMWPE composites. Theoretically, polymers can be strengthened by molecular alignment of the material. When sliding loads are applied to a specimen of UHMWPE, the molecular chains begin to straighten, be untangled, and align in load direction, and the strength tends to increase in this direction. UHMWPE composites can also be further engineered at a micro- or nanometer length scale by blending polymer powder resin with micro- or nanoparticles and fibers before consolidation. UHMWPE composites were reinforced by TiO₂, CNT, kaolin, CF, hydroxyapatite, Al₂O₃, zirconium particles [14–18], and so forth. The works have demonstrated that the addition of optimum amount of nano- and microfibers and ceramic particles into UHMWPE would significantly affect the wear rate under sliding wear conditions.

Recently, the material properties with their own characteristics, applications, advantages, and limitations are important factors for designers and materials engineers. Due to UHMWPE’s complex behaviors, finding an appropriate model for determining the wear properties of UHMWPE can be challenging. The effect of type and weight percentage of fibers and particles in composition and one of the operation parameters such as applied load and sliding speed on wear behavior of UHMWPE was investigated separately. In selecting additive materials, type and percentage for an application are important. The experimental determination of additives for desired wear behavior of UHMWPE composites is cost- and time-consuming. ANN modeling has been used to minimize the experimental study and predict the wear characteristics to establish a correlation between the wear properties and operation parameters of UHMWPE composites. Therefore, the main aim is to determine and understand the effect of type, size, and weight percentage of different reinforcement and variables in operation condition on dry sliding wear properties of UHMWPE composites.

2. Neural Network

The ANNs are a methodology in different applications of materials including prediction of tribological and mechanical properties and were used by many researchers [19–24]. Venkata Rao et al. [25] used ANN to predict surface roughness, tool wear, and amplitude of work piece vibration. They reported that the neural network can help in the selection of proper cutting parameters to reduce tool vibration and tool wear and reduce surface roughness. Gyurova and Friedrich [26] for the prediction of sliding friction and wear properties of polymer composites used ANN and stated that the prediction profiles for the characteristic tribological properties of the ANN exhibited very good agreement with the measured results. Li et al. [27] modeled the sliding wear resistance of the Ni–TiN coatings by using ANN. They explained that the proposed ANN model shows an error of approximately 4.2% and can effectively predict sliding wear resistance of Ni–TiN nanocomposite coatings.

An ANN can be defined as a massively parallel distributed processor storing experiential knowledge and making it available for use [28]. NN is a computational framework that is inspired by biological neural systems. Figure 1 shows the input layer, hidden layer, and the output layer in NN system [29]. It consists of a number of interconnected simple processing units called artificial neurons. The basic structure of an artificial neuron was shown in Figure 2. In ANN modeling, the networks include artificial neurons that consist of three main components, namely, weights, bias, and transfer function.

Figure 1: A typical neural network image.

Figure 2: The basic structure of an artificial neuron [43].

Each neuron receives inputs, attached with a weight , which shows the connection strength for that input for each connection. Each input is multiplied by the corresponding weight of the neuron connection. Next, a bias () value is added to the summation of inputs and corresponding weights () according to the following equation:

The summation is converted as output with an activation (transfer) function, , yielding a value called the unit’s “activation,” as in the following formula:

3. Results and Discussion

NNs are commonly classified according to training algorithms (supervised and unsupervised) and network topology (feedback and feed forward) [30]. BP learning algorithm (Levenberg-Marquardt (Trainlm)) is the most popular and effective supervised learning method used in this study [31, 32]. Sigmoid function, which joins curvilinear, linear, and constant behavior depending on the values of the input, is commonly used as transfer function in NNs [33, 34]. The weight loss of the composites was converted to volume loss, , by dividing it with the specific composite density by the following formula [35]:

where is the weight loss before and after wear test, respectively, and is the density of the composites. In an ANN model, each of the input and output variables was scaled to fall into a range of 0 to 1, using the following scaling formula:

where is the normalized value of the parameter and and are the maximum and minimum values of this parameter, respectively. Output values resulted from ANN also in the range and transformed to its equivalent values based on reverse method of normalization technique [36]. The unnormalized method is as

An extensive literature survey has been performed for collecting the experimental data. Two main processing phases of NN include training and testing. The training process is the adjustment of weights and biases in order to obtain the output through applying a proper method. Hence, the experimental results were divided in two sets, training and testing sets. The training and testing data were randomly selected among experimental results as shown in the Appendix. The input (independent) variables are UHMWPE (wt.%), ZnO (wt.%), zeolite (wt.%), CNT (wt.%), CF (wt.%), GO (wt.%), wollastonite (wt.%), size of ZnO (μm) and zeolite (μm), load (N), and sliding speed (m/s), respectively. The output or dependent variable is volume loss (mm³).

The network architecture and parameters affect the performance of NN. One of the most important duties in NN works is the determination of the numbers of layers and neurons in the hidden layers. In other words, the ANN parameters, such as the number of neurons in the input, network architecture, hidden layer, output layer, learning algorithm, and transfer function, are to be selected for developing an ANN model. There is no well-defined procedure to find the optimal parameter settings and network architecture. The trial and error approach with various numbers of neurons in one hidden layer was used to determine the number of neurons. It was observed that the optimal NN architecture with logistic sigmoid transfer function was 11–12–1 NN architecture. Figure 3 shows the optimal architecture of NN. In the present study, the NN model consists of three layers, which comprises an input layer, a hidden layer, and an output layer.

Figure 3: Optimal NN selection process.

The performance of NN was evaluated by the correlation coefficient () as in the following expression:

Mean absolute error (MAE) and mean square error (MSE) were used as error evaluation criteria in order to facilitate the comparisons between predicted values and desired values according to the following equations:

where is the total number of the datasets and and are the experimental value and predicted output value from the neural network model for a given input, respectively.

The statistical data for the training and testing sets were shown in Table 1. The correlation of NN model with the experimental data for these sets was also shown in Figures 4 and 5.

Table 1: Statistical parameters of training and testing sets.

Datasets

MAE
MSE

Training set
0.9400
3.63
0.389

Testing set
0.9176
4.07
0.412

Figure 4: Correlation of NN and experimental data for training set.

Figure 5: Correlation of NN and experimental data for testing set.

The correlation of coefficients in training and testing sets is 0.9400 and 0.9176 which means that the performance of network model is acceptable. MAE and MSE values of volume loss are 3.63 and 0.389 for training set and 4.07 and 0.412 for testing set. If the MSE reaches zero, the performance of model is regarded as being excellent [37]. Comparison between the test and predicted values shows that the prediction of the proposed NN model is in good agreement with the experimental data and all the errors are within acceptable ranges.

values of training and testing sets are 0.8837 and 0.842, respectively. value compares the accuracy of the model to the accuracy of a trivial assessment model. A high value () tells that all points lie exactly on the curve with no scatter and the results have the perfect correlation. It is clear that all the values are higher than 0.84.

The wear rate of the composites is strongly influenced by many factors, such as the shape and content of reinforcement, operating conditions, the morphologies of surfaces, physical morphology between the matrix material and reinforcement, the bond strength at the matrix/reinforcement interface, and homogeneous distribution of reinforcement [38, 39]. It is difficult to find the effect of each factor on the wear volume loss of the composites and it needs extensive studies. In the current work, the operating parameters and weight percentages and sizes of reinforcement were quantified. Nevertheless, and values of training set indicate that the learning ability of NN is well enough (Table 1 and Figure 4). The effects of the other parameters can be investigated in order to increase the prediction rate of the proposed NN model. It was concluded that the proposed NN model can predict the volume loss of UHMWPE composites containing different particles with size and weight percentages with high accuracy and reliability.

The sensitivity of wear volume loss of UHMWPE composites of each input variable from the minimum to the maximum was given in Figure 6. The sliding speed is an example of factors that can contribute to wear. Our theoretical results demonstrated that the sliding speed has the greatest effect on volume loss of UHMWPE among all input parameters. The different sliding speeds can result in different wear properties. The higher the loading speed is, the more the time UHMWPE will spend in the elastic deformation stage. It is clear that any change in sliding speed, load, UHMWPE (wt.%), ZnO (wt.%), and zeolite (wt.%) will be affected by the volume loss of UHMWPE in comparison to all the other input parameters.

Figure 6: Sensitivity of input vectors.

4. Formulation of NN Model

The main focus is to obtain the explicit formulation of the volume loss as a function of input variables under limited conditions. The ANN models emerged as good candidates for mathematical wear models due to their capabilities in nonlinear behavior, learning from experimental data, and generalization [40]. Hutching’s group [41] and Basavarajappa et al. [42] presented pioneering investigations of ANN techniques for predicting tribological parameters.

As a result, the wear behavior under various parameters was investigated to predict and analyze the relationship between the reinforcements and volume loss of UHMWPE composites. The volume loss () was determined by using the formula

where the parameters are

where , , , , , , , , , , and are normalized values of UHMWPE, ZnO (wt.%), zeolite (wt.%), CNT (wt.%), CF (wt.%), GO (wt.%), wollastonite (wt.%), size of ZnO and zeolite (μm),load (N), and sliding speed (m/s), respectively.

Using derived formulation, the wear volume loss of UHMWPE composite with the size of 1 μm and 5 wt.% ZnO under 10 N load at a sliding speed of 0.033 m/s was determined as 3.093 mm³. In the same experimental conditions, to decrease the wear volume loss to  mm³, the 1 wt.% of zeolite with the size of 45 μm was added according to the NN model theoretically. As a result, the wear volume loss formulation of UHMWPE was evaluated and the two volume loss values were calculated by using this formulation. Additionally, the correlation coefficients of the proposed equations were also evaluated. The correlations of NN, formulation, and experimental data were given in Figure 7.

(a)

(b)

Figure 7: Correlation of (a) NN and formulation and (b) NN and testing set.

It is clear that values of formulation and NN model and formulation and experimental results are 0.9778 and 0.8097, respectively. This means that the proposed NN model (formulation) can predict the volume loss of the composites with 80.97% accuracy.

5. Conclusion

This study proposes an approach of artificial neural network modeling for the wear volume loss in the prediction of UHMWPE composites with different fibers and particles and in various operating parameters. The proposed NN model shows good agreement with the experimental results. Therefore, the explicit mathematical function was derived from ANN models. In the accuracy of the well-trained ANN model, all values for training, testing, and formulation are bigger than 0.80 and the predicted model is of a high reliability rate. The mean absolute error for predicted values does not exceed 4.1%. The sensitivity analysis of the developed NN model demonstrated that sliding speed and applied load are the significant variables in affecting the volume loss. Hence, it was concluded that ANN is a successful and advantageous analytical tool for determining the properties of UHMWPE composites with considerable saving in cost and time.

Appendix

See Table 2.

Table 2: Dataset used NN model.

Reference
UHMWPE
ZnO
(wt.%)
Zeolite
(wt.%)
CNT
(wt.%)
CF
(wt.%)
GO
(wt.%)
Wollastonite
(wt.%)
Load
(N)
Sliding speed
(m/s)
Volume loss
(mm³)

Chang et al. [44]
100
—
—
—
—
—
—
10
0,033
5,699

95
5
—
—
—
—
—
10
0,033
3,093

90
10
—
—
—
—
—
10
0,033
2,075

85
15
—
—
—
—
—
10
0,033
2,329

80
20
—
—
—
—
—
10
0,033
2,413

95
5
—
—
—
—
—
10
0,033
3,781

90
10
—
—
—
—
—
10
0,033
2,218

85
15
—
—
—
—
—
10
0,033
1,962

80
20
—
—
—
—
—
10
0,033
2,091

100
—
—
—
—
—
—
20
0,033
13,333

95
5
—
—
—
—
—
20
0,033
6,101

90
10
—
—
—
—
—
20
0,033
6,440

85
15
—
—
—
—
—
20
0,033
6,927

80
20
—
—
—
—
—
20
0,033
6,541

95
5
—
—
—
—
—
20
0,033
6,358

90
10
—
—
—
—
—
20
0,033
4,150

85
15
—
—
—
—
—
20
0,033
4,965

80
20
—
—
—
—
—
20
0,033
4,611

100
—
—
—
—
—
—
30
0,033
15,914

95
5
—
—
—
—
—
30
0,033
10,225

90
10
—
—
—
—
—
30
0,033
9,159

85
15
—
—
—
—
—
30
0,033
8,582

80
20
—
—
—
—
—
30
0,033
7,613

95
5
—
—
—
—
—
30
0,033
7,905

90
10
—
—
—
—
—
30
0,033
4,722

85
15
—
—
—
—
—
30
0,033
7,172

80
20
—
—
—
—
—
30
0,033
4,986

100
—
—
—
—
—
—
10
0,368
22,151

95
5
—
—
—
—
—
10
0,368
14,435

90
10
—
—
—
—
—
10
0,368
13,094

85
15
—
—
—
—
—
10
0,368
12,566

80
20
—
—
—
—
—
10
0,368
10,723

95
5
—
—
—
—
—
10
0,368
14,092

90
10
—
—
—
—
—
10
0,368
9,874

85
15
—
—
—
—
—
10
0,368
12,382

80
20
—
—
—
—
—
10
0,368
8,096

100
—
—
—
—
—
—
20
0,368
27,742

95
5
—
—
—
—
—
20
0,368
18,818

90
10
—
—
—
—
—
20
0,368
17,029

85
15
—
—
—
—
—
20
0,368
15,631

80
20
—
—
—
—
—
20
0,368
13,993

95
5
—
—
—
—
—
20
0,368
16,326

90
10
—
—
—
—
—
20
0,368
12,665

85
15
—
—
—
—
—
20
0,368
13,669

80
20
—
—
—
—
—
20
0,368
11,312

100
—
—
—
—
—
—
30
0,368
29,032

95
5
—
—
—
—
—
30
0,368
22,255

90
10
—
—
—
—
—
30
0,368
17,816

85
15
—
—
—
—
—
30
0,368
17,347

80
20
—
—
—
—
—
30
0,368
15,923

95
5
—
—
—
—
—
30
0,368
17,271

90
10
—
—
—
—
—
30
0,368
13,309

85
15
—
—
—
—
—
30
0,368
15,324

80
20
—
—
—
—
—
30
0,368
12,867

100
—
—
—
—
—
—
10
1,022
23,226

95
5
—
—
—
—
—
10
1,022
14,435

90
10
—
—
—
—
—
10
1,022
13,952

85
15
—
—
—
—
—
10
1,022
10,482

80
20
—
—
—
—
—
10
1,022
9,543

95
5
—
—
—
—
—
10
1,022
14,350

90
10
—
—
—
—
—
10
1,022
13,666

85
15
—
—
—
—
—
10
1,022
15,018

80
20
—
—
—
—
—
10
1,022
9,704

100
—
—
—
—
—
—
20
1,022
27,527

95
5
—
—
—
—
—
20
1,022
31,277

90
10
—
—
—
—
—
20
1,022
22,682

85
15
—
—
—
—
—
20
1,022
20,657

80
20
—
—
—
—
—
20
1,022
18,818

95
5
—
—
—
—
—
20
1,022
26,895

90
10
—
—
—
—
—
20
1,022
22,825

85
15
—
—
—
—
—
20
1,022
24,458

80
20
—
—
—
—
—
20
1,022
16,942

100
—
—
—
—
—
—
30
1,022
53,333

95
5
—
—
—
—
—
30
1,022
84,207

90
10
—
—
—
—
—
30
1,022
58,958

85
15
—
—
—
—
—
30
1,022
60,500

80
20
—
—
—
—
—
30
1,022
58,171

95
5
—
—
—
—
—
30
1,022
42,361

90
10
—
—
—
—
—
30
1,022
39,067

85
15
—
—
—
—
—
30
1,022
30,465

80
20
—
—
—
—
—
30
1,022
33,348

Chang et al. [45]
100
—
—
—
—
—
—
10
0,209
2,800

90
—
10
—
—
—
—
10
0,209
2,200

80
—
20
—
—
—
—
10
0,209
2,200

100
—
—
—
—
—
—
20
0,209
5,000

90
—
10
—
—
—
—
20
0,209
3,600

80
—
20
—
—
—
—
20
0,209
3,500

100
—
—
—
—
—
—
30
0,209
5,900

90
—
10
—
—
—
—
30
0,209
4,700

80
—
20
—
—
—
—
30
0,209
4,700

100
—
—
—
—
—
—
10
0,419
4,700

90
—
10
—
—
—
—
10
0,419
3,900

80
—
20
—
—
—
—
10
0,419
3,100

100
—
—
—
—
—
—
20
0,419
6,500

90
—
10
—
—
—
—
20
0,419
6,000

80
—
20
—
—
—
—
20
0,419
5,200

100
—
—
—
—
—
—
30
0,419
8,100

90
—
10
—
—
—
—
30
0,419
7,900

80
—
20
—
—
—
—
30
0,419
6,200

100
—
—
—
—
—
—
10
0,838
8,000

90
—
10
—
—
—
—
10
0,838
5,900

80
—
20
—
—
—
—
10
0,838
5,000

100
—
—
—
—
—
—
20
0,838
9,800

90
—
10
—
—
—
—
20
0,838
9,000

80
—
20
—
—
—
—
20
0,838
7,000

100
—
—
—
—
—
—
30
0,838
11,000

90
—
10
—
—
—
—
30
0,838
10,500

80
—
20
—
—
—
—
30
0,838
8,900

Zoo et al. [18]
100
—
—
—
—
—
—
5
0,300
0,376

99,9
—
—
0,1
—
—
—
5
0,300
0,268

99,8
—
—
0,2
—
—
—
5
0,300
0,134

99,5
—
—
0,5
—
—
—
5
0,300
0,021

Dangsheng [14]
100
—
—
—
—
—
—
196
0,420
1,820

95
—
—
—
5
—
—
196
0,420
1,400

90
—
—
—
10
—
—
196
0,420
1,350

85
—
—
—
15
—
—
196
0,420
1,110

80
—
—
—
20
—
—
196
0,420
0,730

70
—
—
—
30
—
—
196
0,420
0,590

Tai et al. [46]
100
—
—
—
—
—
—
5
0,090
0,043

99,9
—
—
—
—
0,1
—
5
0,090
0,038

99,7
—
—
—
—
0,3
—
5
0,090
0,033

99,3
—
—
—
—
0,7
—
5
0,090
0,028

99
—
—
—
—
1
—
5
0,090
0,028

98
—
—
—
—
2
—
5
0,090
0,026

97
—
—
—
—
3
—
5
0,090
0,025

Tong et al. [47]
100
—
—
—
—
—
—
120
0,530
1,73

95
—
—
—
—
—
5
120
0,530
1,31

90
—
—
—
—
—
10
120
0,530
1,2

85
—
—
—
—
—
15
120
0,530
1,58

80
—
—
—
—
—
20
120
0,530
1,8

90
—
—
—
—
—
10
40
0,530
0,25

90
—
—
—
—
—
10
80
0,530
0,7

90
—
—
—
—
—
10
160
0,530
2,28

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

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