**1. Introduction**

In the study of tribology, highly nonlinear and very complex relationship exists. Specific wear rate of materials especially polymer matrix composites emanates from scores of intricate associations on both microscopic and macroscopic levels between surfaces which are in contact [1]. These associations depend upon tribological,

geometrical as well as material behaviors of the contacting surfaces and the sliding conditions for example, temperature, type of contact, lubricating conditions, applied load, etc. [2]. Simulation of tribological properties usually deals with building of mathematical models extracted from practical data. The numbers of these models were obtained to simulate specific wear rate of materials under restricted conditions. Yet, no distinctive model was universalized to reveal the specific wear rate of polymer matrix composites.

Of recent soft computing techniques such as artificial neural networks (ANNs) and adaptive neuro fuzzy inference system (ANFIS) have emerged as potential and effective tools to model wear property of poly-based composites, owing to their abilities to learn from experimental data and generalize [3]. The pioneering studies of exploring the potentials of these soft computing methods especially ANN in the prediction of wear properties were carried out by Hutching et al. and Jones, Jensen and Fusaro [4, 5], respectively. Thereafter, many researchers applied the methods to analyze and predict the wear property polymer matrix composites under different test conditions and material compositions. In the physical experimentation of wear simulation, known material compositions and properties, experimental parameters are fed into the ANN and ANFIS models as inputs and the anticipated specific wear rate responses of the virtual scenario are computed. The fundamental advantage of ANN and ANFIS modeling in comparison to other modeling techniques are in their capabilities to provide accurate approximations or predictions when complexity and nonlinearity are involved at the same time. Complexity and nonlinearity cannot be handled by traditional curve fits [1]. More so, ANN and ANFIS models can effectively deal with these.

Velten, Reinicke and Friedrich [6] explored the potential of ANN when they predicted wear volume of short fiber reinforced polymeric composites. They found that with increase in the number of inputs the prediction quality of the ANN model was improved. Zhang, Friedrich and Velten [7] used multilayered feed forward neural network to predict the coefficient of friction and specific wear rate of short fiber reinforced polyamide. The results indicated a good agreement with experimental results. Jiang, Zhang and Friedrich [8] applied ANN model to predict both the wear and mechanical properties of polymer matrix composites. They established a 3D plots to investigate the properties of the materials based on the material constitutions and the experimental conditions. They reported that a well-trained ANN could model the wear and that the results of the model were in good agreement with the computed results. Aleksendric and Duboka [9] used ANN method to predict the automotive friction material features at room temperature. Five different types of friction materials were fabricated and experimented for the prediction purpose and the ANN was trained with five different learning algorithms. They found that each learning algorithm performed differently from one another but concluded that Bayesian regularization algorithm produced the best result with a single layer. Aleksendric and Duboka [10] applied the ANN to look into the possibilities of prediction wear property of friction composites at elevated temperature. They reported that ANN was effective in prediction the wear behavior of the materials as its results were in good agreement with the experimental ones. Jiang et al. [11] predicted wear and mechanical properties of polyamide composites, Varade and Kharde [12] predicted the wear behavior of PTFE glass-fiber reinforced composite using ANN and Taguchi technique. They found that ANN performed better than that of conventional Taguchi method.

Mesbahi, Semnani and Khorasani [13] employed adaptive neuro fuzzy inference system (ANFIS) to investigate the specific wear loss of PTFE, graphite short carbon fiber and nano-TiO2. They reported that ANFIS model performed better than ANN model. Jarrah, Al-Assaf and El Kadi [14] used ANFIS to model the fatigue property

*Specific Wear Rate Modeling of Polytetraflouroethylene Composites via Artificial Neural… DOI: http://dx.doi.org/10.5772/intechopen.95242*

of unidirectional glass/fiber epoxy composite subjected to tension-tension and tension-compression conditions. They reported that the results of the ANFIS model were better when compared to those of ANN technique. Vassilopoulos and Bedi [15] applied ANFIS to model and predict the fatigue behavior of multidirectional laminate composite. They reported that about 50% of the data was adequate to model and predict the fatigue behavior of the composite and the results were in agreement with the actual data.

From above, it can be established that ANN and ANFIS models, hold great potentials and are promising tools in the modeling of complex and nonlinear wear behavior of polymer-based composites. The aim of this study is to model and predict the specific wear rate (SWR) of polytetraflouroethylene (PTFE) reinforced with glass, carbon and bronze fibers. The results of the ANN and ANFIS models were then compared with multilinear regression (MLR) model to affirm their superiority to traditional curve fit.

### **2. Methodology**

ANN and ANFIS models have exhibited great power in describing complex, noisy and nonlinear phenomenon like specific wear rate. In this study, specific wear rate of PTFE composites was modeled and predicted using ANN, ANFIS and MLR models with density, volume fraction, sliding distance, sliding speed and load as inputs while specific wear rate as output. PTFE is a synthetic flouropolymer of tetrafluoroethylene that possesses superior characteristics due to its molecular structure consisting of fluorine and carbon. PTFE is hydrophobic and exhibits low wear resistance because of its soft nature making its suitable for use as a single material for practical application [16]. Glass fiber (GF) is a material consisting of several fine fibers of glass. GF is less brittle, less strong and cheaper than carbon. GF is compatible with most of the synthetic resin, does not rot and remain unaffected by the action of rodents and insects. Carbon fiber (CF) is composed of thin, strong crystalline filament of carbon and has a diameter of about 5–10 μm in diameter. It is very strong, stiff, and light; its strength is five times that of steel and twice as stiff. When CF is added to polymer, it improves the tribological property of the polymer [17]. Bronze fiber (BF) is a metal fiber that consists of 88% of copper and 12% of tin. It is hard and brittle. Its properties depend on the composition of the alloying tin.

A total of 63 specific wear rate experimental dataset was collected from the works conducted by [18, 19]. Some mechanical and physical properties of the materials are as shown in **Table 1**.

#### **2.1 Artificial neural network (ANN)**

ANN is a computational technique based on mimicking the function of the biological neurons [20]. Three properties are employed in differentiating various ANN models which are learning algorithms, transfer function as well as network


**Table 1.**

*Some physical and mechanical properties of the PTFE reinforced composites.*

architecture [21]. The principal parts of ANN are the nodes or neuron which process the data and the interconnections that show the interconnection power connected to numeric weights [21, 22]. **Figure 1** shows the input, hidden and output layers of ANN architecture [23]. The fundamental structure of the neuron is as indicated in **Figure 2**. Each neuron receives input data, assigns weight wito the input data that indicates the connection power for that input data for each connection. Thereafter, a bias bi value is added to the total addition of the input data and corresponding weights uð Þ in accordance with (Eq. (1)).:

$$\mathbf{u}\_{\mathbf{i}} = \sum\_{\mathbf{j}=1}^{N} \mathbf{w}\_{\mathbf{i}} \mathbf{x}\_{\mathbf{j}} + \mathbf{b}\_{\mathbf{i}} \tag{1}$$

where xi is the input data, j is the jth data, wi represents the weight, bi shows the bias and N stands for the total number of the data points.

The summation is transformed into output with the aid of a transfer (an activation) function F uð Þ<sup>i</sup> , generating a value referred to as the unit's "activation", as provided in the (Eq. (2)).

**Figure 1.** *A classical ANN image.*

**Figure 2.** *The fundamental configuration of an artificial neuron.*

*Specific Wear Rate Modeling of Polytetraflouroethylene Composites via Artificial Neural… DOI: http://dx.doi.org/10.5772/intechopen.95242*

$$\mathbf{O} = \mathbf{f}(\mathbf{u}\_i) \tag{2}$$

where O is the output.

One of the common types of ANN is the feed-forward neural network (FFNN). In FFNN technique, the processing layer is completely interrelated by weights to the rest of the processing layers (neurons). The learning stage in FFNN is actualized by back-propagation (BP) algorithm. The idea of using the BP algorithm is to compute the optimum weights that lead to the production of the target data in accordance with a chosen accuracy. In this paper, FFNN was applied due to its unique superiority of generating exclusive solutions without any prior knowledge of the mathematical computations in the parameters. **Figure 3** shows the architecture of a FFNN used in this study. The ability of ANN to learn by example makes it suitable for solving complex and nonlinear behavior such as specific wear rate that cannot be addressed by conventional mathematical or physical models [24].

#### **2.2 Adaptive neuro fuzzy inference system (ANFIS)**

ANFIS is an important neurological network technique to obtain result of function approximation questions integrating the adaptive neural network and fuzzy inference system. As a global estimator, ANFIS was designed to surmount the limitations of FIZ and ANN. ANFIS integrates the experience capability of neurological network and the merits of the rule-based fuzzy structure, which can assimilate previous information into categorization mechanism. A structure is constructed by fuzzy logic descriptions as well as the neurological network is utilized to harmonize the structure variables naturally thus removing the demand for manual perfection of the fuzzy structure variables not like the neurological network where the structure is constructed by training. Adaptive ability and flexibleness of ANFIS makes it effective in handling the unpredictability of processes. The ANFIS architecture is made up of five different layers arranged like any multiple layer FFNN; coded in accordance with their operational functions. Sugeno firs-order fuzzy model had been applied in this paper. Different from ANN whereby weights are attuned, determination of the fuzzy language rules is needed as training the ANFIS model. The training of the membership function variables of the ANFIS is actualized through back propagation and/or least square and variables of the Takagi

**Figure 3.** *ANFIS and first-order Sugeno FIS model configuration.*

Sugeno fuzzy model are trained by the conventional square technique. The overall output of the ANFIS structure is described as a linear combination of the consequent variables. The common representation of an ANFIS model is demonstrated in **Figure 4** using two input variables.

Supposing fuzzy inference system with two inputs and one output as x, y and f, a Sugeno fuzzy first order, the rules are thus:

$$\text{Rule } (\mathbf{1}): \text{If } \boldsymbol{\mu}(\mathbf{x}) \text{ A}\_1 \text{ and } \boldsymbol{\mu}(\mathbf{y}) \text{ is } \mathbf{B}\_1; \text{ then } \mathbf{f}\_1 = \mathbf{p}\_1 \mathbf{x} + \mathbf{q}\_1 \mathbf{y} + \mathbf{r}\_1 \tag{3}$$

$$\text{Rule (2)}: \text{If } \mathfrak{\mu}(\mathbf{x}) \text{ A}\_2 \text{ and } \mathfrak{\mu}(\mathbf{y}) \text{ is } \mathbf{B}\_2; \text{ then } \mathbf{f}\_2 = \mathbf{p}\_2 \mathbf{x} + \mathbf{q}\_2 \mathbf{y} + \mathbf{r}\_2 \tag{4}$$

Membership functions parameters for x and y inputs are A1,B1, A2, B2 outlet functions' parameters of f are p1, q1, r1, p2, q2, r2, a five-layer neurological network arrangement possess the expression and configuration of ANFIS as:

First layer: Every node I is an adaptive node in this layer that contain the nodal function as:

$$\mu\_{\rm i}^{1} = \mu\_{\rm Ai}(\mathbf{x}) \text{ for } \mathbf{i} = \mathbf{1}, \mathbf{2} \text{ or } \upmu\_{\rm i}^{1} = \mu\_{\rm Bi}(\mathbf{x}) \text{ for } \mathbf{i} = \mathbf{3}, \mathbf{4} \tag{5}$$

Where ψ<sup>1</sup> <sup>i</sup> is for input x or y is the membership grade. Gaussian membership function had been selected in this paper because of its minimum prediction error.

Second layer: T-norm operator links every rule in this layer between inputs 'AND' operator thus:

$$
\mu\_{\rm i}^2 = \beta\_{\rm i} = \mu\_{\rm Ai}(\mathbf{x}) \times \mu\_{\rm Bi}(\mathbf{x}) \text{ for } \mathbf{i} = \mathbf{1}, \mathbf{2} \tag{6}
$$

Third layer: "Normalized firing strength" is the output of this layer:

$$\mathbf{w}\_{\mathbf{i}}^{3} = \boldsymbol{\varpi} = \frac{\mathbf{W}\_{\mathbf{i}}}{\mathbf{W}\_{1} + \mathbf{W}\_{2}} \text{ i = 1, 2} \tag{7}$$

Fourth layer: Each node i in the fourth layer is an adaptive node and executes the consequent of the rules as follows:

$$
\Psi\_{\mathbf{i}}^{4} = \varpi (\mathbf{p}\_{\mathbf{i}} \mathbf{x} + \mathbf{q}\_{\mathbf{i}} \mathbf{y} + \mathbf{r}\_{\mathbf{i}}) \tag{8}
$$

**Figure 4.** *ANFIS and first-order Sugeno FIS model configuration.*

*Specific Wear Rate Modeling of Polytetraflouroethylene Composites via Artificial Neural… DOI: http://dx.doi.org/10.5772/intechopen.95242*

ϖ describes the output of layer 3 and pi , qi , r1are the consequent parameters. Layer 5: Here the overall output of all incoming signals is calculated in this layer as:

$$\mathbf{w}\_{\mathbf{i}}^{\mathbf{g}} = \varpi \left( \mathbf{p}\_{\mathbf{i}} \mathbf{x} + \mathbf{q}\_{\mathbf{i}} \mathbf{y} + \mathbf{r}\_{\mathbf{l}} \right) = \sum \mathbf{w}\_{\mathbf{i}} \mathbf{f}\_{\mathbf{i}} = \frac{\sum \mathbf{w}\_{\mathbf{i}} \mathbf{f}\_{\mathbf{i}}}{\sum \mathbf{w}\_{\mathbf{i}}} \tag{9}$$

#### **2.3 Multi linear regression (MLR) model**

Linear regression analysis is a conventional technique used in applied science fields to describe and examine different parameters. Regression analysis especially aids in comprehending how the standard values of the dependent parameter varies as independent parameters vary, whilst the other independent parameters are held constant; examines the correlation between these parameters. The equation below was obtained from the regression analysis.

$$\text{SWR} = 0.162 + 0.269 \text{L} + 0.369 \text{D} - 0.293 \rho + 0.347 \text{V} + 0.041 \text{7S} \tag{10}$$

where SWR is the (specific wear rate), L = applied load, D = sliding distance, ρ = density, V volume fraction of reinforcement and S = sliding speed.

#### *2.3.1 Sensitivity analysis*

In order to find the parameter that greatly influences the specific wear rate of the composites, nonlinear sensitivity analysis was conducted using neural network. In the sensitivity analysis each of the input parameter was used to predict the specific wear rate of the composites through the FFNN model. The performance of the individual model was assessed based on training and testing stages of the modeling. The mean value of the prediction performance criterion of each model obtained in both training and testing phases was then used to rank the contribution of the parameters to the specific wear rate of the composites.

#### *2.3.2 Data pre-processing and performance evaluation*

The data used in this study was normalized between zero (0) and unity (1) using the (Eq. (11)). The normalization was done to prevent bigger data values from overshadowing the smaller ones. Besides, data normalization simplifies the numerical computations in the model which in turn improves the prediction quality of the model and reduces the time taken to achieve global minimum.

$$
\lambda\_{\text{norm}} = \frac{\lambda - \lambda\_{\text{min}}}{\lambda\_{\text{max}} - \lambda\_{\text{min}}} \tag{11}
$$

Where λnorm is the normalized mass loss value, λmin, and λmax represent actual, minimum and maximum mass loss values of the data, respectively.

The data was split into training data and testing data. The training data was used to adjust the weights of all the linking neurons until the required error level was attained. Consequently, the network performance is evaluated by using the testing data. The prediction performance is determined using Nush-Scutcliffe or determination coefficient (DC) and root mean square error (RMSE). DC indicates fitness of the observed data and lies between -∞ to 1 while RMSE measures the difference between actual and predicted values and ranges from 0 to 1. Higher B and lower RMSE indicate efficient model and vice versa. DC and RMSE are given in (Eq. (12)). and (Eq. (13))., respectively.

$$\text{DC} = 1 - \frac{\sum\_{i=1}^{n} \left(\lambda\_{\text{acti}} - \lambda\_{\text{predi}}\right)^2}{\sum\_{i=1}^{n} \left(\lambda\_{\text{acti}} - \overline{\lambda}\_{\text{acci}}\right)^2} \tag{12}$$

$$\text{RMSE} = \sqrt{\frac{\sum\_{i=1}^{n} \left(\lambda\_{\text{active}} - \lambda\_{\text{predi}}\right)^2}{\mathbf{N}}} \tag{13}$$

Where N is number of observations, λacti stands for actual values, λpredi represents the predicted values and λacti is the mean value of the actual values.
