Estimation of adhesive wear behavior of the glass fiber reinforced polyester composite materials using ANFIS model

Abstract

Glass fiber reinforced polyester (GFRP) composite materials are widely used in various applications. The prediction of wear values for composite materials is very complex and nonlinear phenomena. Artificial intelligence methods (AI) and expert systems such as artificial neural networks (ANNs) and fuzzy inference systems (FIS) have a series of properties on modeling nonlinear systems. In some situations, ANNs are insufficient under abrupt changes in input variables. Adaptive Neuro Fuzzy Inference System (ANFIS) is capable of integrating the linguistic expressions of FIS with the adaptation and learning skills of the ANNs. The aim of this study is to determine the optimum material content and working conditions in terms of wear resistance. This study proposes an ANFIS sub-clustering based prediction model for estimation of wear behavior of GFRP composites within various concentrations of materials and under diverse loads and speeds. Proposed ANFIS model extracted optimum concentrations and operating parameters to obtain the minimum wear rate. Due to the wear rate estimation model, optimum wear rate value is reached to 25.0013 (mm³/Nm)*10⁻⁶ at CaCO₃, polystyrene, glass fiber, glass bead, alumina, load and speed values of 49%, 0%, 11%, 10%, 0.8%, 10 N and 100 rpm respectively. A high estimation capability (R² = 0.964) has been achieved using ANFIS Model.

Keywords

Glass fiber reinforced polyester ANNs ANFIS adhesive wear composite material

Introduction

In the last decades, rising of industrial demands for material technology has brought about the requirement of new materials with high durability. Wear analysis which indicates the strength of a material is getting significant. Adhesive wear of polymer composites is a complicated wear process which is significantly affected by operational situations and composite material properties. Surface roughness, wear rate, friction coefficient are main indicators of wear on a material. The wear causes to surface roughness, weakening of components, surface degradation and shortening functional lifecycle of components. Since such kind of effects cause to failures in manufacturing applications, polymer-based composites and their wear resistance property became essential.

Glass fiber reinforced polyester (GFRP) composite materials are widely used in various applications because of their high specific strength, high chemical resistance, low weight, excellent elasticity, high corrosion resistance and high thermal stability. GFRP composites may also contain additives and fillers. They may contain thermoplastic tensile additives such as polystyrene, polyvinyl acetate and plasticizers.

In the literature, there are a number of studies of the artificial intelligence methods in estimating the wear properties of the materials. Mathematical models which predict wear rate by determining the material loss under solid particle impact conditions allows us to repeat several experimental tests.¹ However, prediction of wear values for composite materials is very complex and nonlinear phenomena. Artificial intelligence methods (AI) and expert systems such as artificial neural networks (ANNs) andfuzzy inference systems (FIS) have a series of properties on modeling nonlinear systems. ANNs can establish a multivariable and continuous behavior approximation of nonlinear processes and maps a relation between the process inputs and outputs. They also can make discrete approximation of a function, called “classification” which extracts functioning conditions of a machine. In this purpose, a three layered ANNs structure is proposed for prediction of erosion wear characteristics of a material whose inputs and output are; erodent discharge rate, iron mud content, impingement angle, erodent velocity and erosion rate, respectively.² ANNs are used to estimate wear on C120 and Rp3 steel surfaces reinforced with short glass fibers, under linear contact.³ These composite mixtures result in nonlinearity in the machining³ processes and make difficulties in wear predictions with analytical models under different pressures and speeds. Similarly, wear rate optimization of composites such as epoxy + E-glassfiber + carbon particles is carried out by ANN prediction model which reduces performance measures such as friction coefficient and weight loss.⁴

Implementation of Genetic Algorithm (GA) and multiple linear regression analysis (Taguchi Method) for tuning ANNs parameter successfully improve the wear rate of composites.⁵ A similar study which addresses ANNs computation for simulation and prediction of erosive wear response in Linz–Donawitz slag (LDS) filled epoxy-glass fiber composites; took impact velocity, impact angle, erodent size and temperature into account.⁶ The authors had analysed effects of impact angle and impact speed thoroughly in another study. Taguchi’s approach for orthogonal arrays allows to find optimal parameter settings for minimization of wear rate.⁷ In another study, Padhi and Satapathy carefully observe the morphology of worn surfaces, such as fracture of short glass fiber, plastic deformation level, wear track etc. under electron microscopy and validated the significant capability of a well-trained ANNs with experimental results.⁸ A procedure which combines planning of experiments with D-optimal mixture design (DMD) method and effective optimization of analysing methods such as ANNs, genetic algorithms (GA) and simulated annealing is proposed to assist decision making of experts in determination of optimal ratio of ingredients in the mixture of polytetrafluoroethylene (PTFE) reinforced polycarbonate(PC) short glass fibers (SGF) composites.⁹ In another study, effect of mass percentage of graphite filler content in cotton fiber polyester composite (CFPC) to wear behavior was observed by considering the impact of operating parameters such as speed, load, fiber volume fraction, sliding distance and sliding velocity. Wear is acceptably predicted by regression models and ANNs model.¹⁰ Dry friction wear testers determine abrasive wear levels. ANNs and particle swarm optimization (PSO) based prediction tools estimates tribological and mechanicalproperties; such as abrasion resistance, impact energy, tensile modulus and hardness; of the composites. These two artificial intelligence methods unveil that wear is directly proportional to load and sliding velocity.² Specific wear rate of TiO₂ filled polyester-based composite is found out by ANNs methods. Statistical significance of factors is determined by analysis of variance (ANOVA) from experimental data and sliding velocity is found to be the main factor that affects the wear rate.¹¹ A Neural Network based computational model, designed to estimate the dry sliding wear of epoxy composites reinforced by pine wood, predicts that filler content, sliding velocity and normal load are the major factors of the wear.¹² ANN models’ performances for the friction coefficient estimation are compared in details by consideration of previous and current studies.¹³

ANNs could imitate nonlinear behavior and could learn a generalization from experimental results. Through the different algorithms, Levenberg-Marquardt (LM) training algorithm was found to be more successful in estimation refer to all others.¹⁴ In this way, ANNs estimated wear loss refers to filler content, load and sliding distance within maximum %5 error. In the wear estimation of Cu-SiC-Gr hybrid composites, different structures of ANNs trained with and without GA.¹⁵ Prediction models of ANNs provide to avoid from wasting material, experimental costs and testing time. In some situations, ANNs are insufficient under abrupt changes in input variables. In order to interpolate an enormous differentiation, ANNs can converge to an extremely negative or positive peak value. Fuzzy rules can establish separately the roof of rapid changes in a nonlinear behavior. Following the roof structure, ANNs can be addressed for optimization of the rules and membership functions (MFs). The relation between inputs and corresponding outputs are established by a Fuzzy Inference System (FIS).¹⁶ Adaptive Neuro fuzzy Inference System (ANFIS) is built on a specific structure of first order Takagi-Sugeno (T-S) Type Fuzzy Inference System.¹⁷ FIS do not include any learning capability so as to reduce output error cost function and to choose appropriate network’s structure. That’s why, multilayer feed forward artificial neural networks are applied on the structure in order to fine tuning the parameters of MFs.¹⁸ ANFIS is capable of integrating the linguistic expressions of FIS with the adaptation and learning skills of the ANNs.¹⁹

The ANFIS is a reliable artificial intelligence (AI) method used as a prediction model which assembles a nonlinear relationship between cutting forces and corresponding roughness responses.^16,20,21 A study on prediction of surface roughness of machining steel (11SMnPb30) refer to cutting forces such as spindle speed, feed rate, etc. indicates the highly estimation capability (R² = 0.95) of the ANFIS method.²² Characterization of dry surface contacts among alloyed steel and reinforced plastic material is modelled by ANFIS and it successfully estimated the wear.²³ In the study, FIS’s of the ANFIS model are generated by three alternative optimization methods that are; sub-clustering, fuzzy c-means and grid partitioning methods. In the burnishing process of cylindrical polyoxymethylene, surface roughness and hardness are predicted by an ANFIS model in accuracies of 97% and 96%, respectively.²⁴ Predictive AI models can determine exact wear behavior modeling of a certain material such as hardened steel. When three different AI techniques (ANFIS, FIS and ANNs) are compared for the mentioned problem, all techniques proved high accuracies, but ANNs provide the best performance.²⁵

In this study, samples produced from GFRP material were subjected to adhesive wear test. The aim of this study is to determine the optimum material content and operating parameters in terms of wear resistance. In literature, the studies generally compared ANNs estimation model and experimental results. ANNs models commonly take load, speed and percentage additive amount in the composite (%) into account. This study proposes an ANFIS sub-clustering based prediction model for estimation of wear behavior of glass fiber reinforced polyestercomposites within various concentrations of materials and under diverse loads and speeds. The model extracted optimum concentrations and operating parameters to obtain the minimum wear rate.

Materials and methods

Tested materials

The high performance products can be obtained by combining different ingredients in GFRP composite materials. One of these products is Bulk molding compound (BMC). BMC is composite generally containing unsaturated polyester (UP) resin as the matrix, glass fibers as reinforcement and other ingredients such as catalysts, particulate fillers, thickening agents and mold release agents.²⁶ The main components in the BMC composition are unsaturated polyester resin, glass fiber and CaCO₃ used in high proportions. Apart from the main ingredients, different materials such as polystyrene to reduce the volumetric shrinkage of the resin, alumina and glass beads to improve material properties were added to the BMC. Wear resistance can be increased by using hard filling materials in polymer-based composite materials. In different studies in the literature, it has been reported that alumina and glass beads reduce the wear rate.^27–30 In this study, it was aimed to observe the effects on the wear behavior by including alumina and glass beads in the chemical composition.

The chemical compositions of GFRP samples using in experimental study are presented in Table 1.

Table 1.

Compositions of GFRP Samples.

Sample	Matrix	Reinforcement	Filler
D1	20 wt.% orthophthalic polyester	40 wt.% GF	10 wt.% GB 30 wt.% CaCO₃
T1	20 wt.% orthophthalic polyester	11 wt.% GF	1 wt.% Alumina 68 wt.% CaCO₃
T2	20 wt.% orthophthalic polyester 8 wt.% polystyrene tensile additive	11 wt.% GF	1 wt.% Alumina 60 wt.% CaCO₃
T3	20 wt.% orthophthalic polyester 8 wt.% polystyrene tensile additive	11 wt.% GF	5 wt.% GB 56 wt.% CaCO₃
T4	20 wt.% orthophthalic polyester	11 wt.% GF	1 wt.% Alumina 5 wt.% GB 63 wt.% CaCO₃
T5	20 wt.% orthophthalic polyester 8 wt.% polystyrene tensile additive	11 wt.% GF	1 wt.% Alumina 5 wt.% GB 55 wt.% CaCO₃

In this study, the orthophthalic polyester resin are used as resin matrix material in GFRP samples. Glass bead (GB), calcium carbonate (CaCO₃) and alumina are used as filler materials in GFRP samples. Polystyrene is used as tensile additive material in polyester resin. Glass fiber (GF) is used as reinforcement material. Glass fiber and filler materials are used in specific proportions in glass fiber reinforced polyester materials. The causes for the usage mounts of glass fiber and fillers in the GFRP material are summarized below.

a-Glass fiber

In general, 10–30 wt% glass fibers are used as there enforcing material in the GFRP materials.²⁷ In this study 11–40 wt% glass fiber reinforcement was used to increase the mechanical properties of GFRP composite material.

b-Polystyrene

In order to avoid residual stresses in unsaturated polyester resins, tensile additives are used in the range from 0 to 10wt%.²⁶ Since the dimensions of test specimen in this study are small, the polystyrene tensile additive was also especially preferred at a low rate (8%).

c-Alumina

Alumina is used in small amounts (1%) as filler in GFRP composites because its cost is higher than that of CACO_3.²⁸

d-CaCO₃

CACO₃ is the major and the economical filler material in GFRP materials. In studies carried out in the literature, the CaCO₃ use is between 40 and 80 wt%.²⁶ In this study, after using polyester resin, glass fibers, alumina and glass beads, the remaining parts of the BMC component were completed with CaCO₃ filling material ranging from 30 to 68 wt%.

e-Glass beads

The glass beads are used in polyester composites between 0 and 10 wt% in literature studies.³⁰ In this study, glass beads were used in 5 wt% and 10 wt%.

Wear testing procedures

The adhesive wear test of samples was carried out on ball on disc wear testing machine (Figure 1). In tribometer, the ceramic ball with radius of 3 mm was fixed on the load arm and sample was placed on a rotating disc with a friction radius of 5 mm. In the experiments, the samples were subjected to two different speeds (n = 100 rpm, n = 200 rpm) and two different loads (F = 10 N, F = 20 N) at constant sliding distance (150 m). Each sample was tested at least three times. Wear traces were investigated by Nikon SMZ 745 T light microscope. The wear rate values of samples were calculated according to test results.

Figure 1.

Adhesive wear test mechanism.

The volume loss values of samples were calculated according to ASTM G99-05 as following. It was not taken into consideration since the wear in the ball was not significant.³¹

V = \frac{π . R . D^{3}}{6. r}

Here V is volume loss (mm³), R is friction radius (5 mm), D is the wear trace width (mm) and r is the ball radius (3 mm).

The wear rate values of samples were calculated by following equation³²:

k = \frac{V}{L . X}

Here L is the applied load (N), X is the sliding distance (150 m) and k is the wear rate (mm³/Nm).

Architecture of ANFIS

Intelligent systems which combine pattern recognition and adaptation ability of ANNs with human knowledge based FIS are called neuro-fuzzy systems.³³ There are several methods which successfully combine strengths of Artificial Neural Networks (ANNs) and Fuzzy Logic (FL). Adaptive networks are composed of unit nodes connected by forward connections, in which each unit performs a particular function of Fuzzy Inference System (FIS).³⁴ Unlike ANNs, no weights are associated with the connections. Connections only identify the direction of signal flow from one to the following units.

In the ANFIS Structure, the parameters of antecedent and consequent units perform the task of the weights.¹⁷ Adjusting these parameters, the unit functions as well as the general behavior of the ANFIS, are altered. By means of input-output training data, ANFIS builds a FIS whose membership functions (MF) parameters are incorporated with the optimization of MFs along with the learning process. The parameters are acting like weights of ANNs. Back propagation or hybrid methods are addressed for adjusting the parameters and they provide FIS to learn the input-output relation of a system.³⁵ A first order ANFIS Model with 9 Rules is given in Figure 2 where x and y are inputs and z is output of the system.

Figure 2.

First order ANFIS model with nine rules.

Following the input layer, there are five layers each of which is specialized for different tasks. There are two main procedures: the first stage is a forward calculation which calculates inputs and processed it in the forward direction and yields an output where second stage optimizes the parameters refer to the error between actual output and desired output values.

Forward calculations

Inference part of the system is a kind of Takagi-Sugeno³⁶ Fuzzy Inference System (FIS) procedure, where calculations are in the forward direction. Figure 2 illustrates the forward system architecture composed of one input and five output layers, which are input, fuzzy, product, normalized, de-fuzzy and total output layers. Training set adjusts input and output fuzzy membership function parameters by means of several optimization methods such as back propagation algorithm, etc.

Input layer

Input x and y are fuzzified and converted to fuzzy sets and their supporting degrees. For this purpose, sigmoid functions (equation (3)) and gauss functions (equation (4)) are utilized in the borderlines and inside respectively.

μ_{\underset{~}{A}} (x) = \frac{1}{(1 + e^{- (x - m) σ})}

where m is center of the sigmoid functionand and σ is slope of the sigmoid function.

Furthermoresign of σ determinesdirection of theslope. Similarly, gauss function can be realized as (equation (4)).

μ_{\underset{~}{A}} (x) = e^{- \frac{{(x - c)}^{2}}{2 σ^{2}}}

where c and σ is center and width of gauss function, respectively.

Hidden layers

1’st layer (fuzzy layer): Outputs for the input layer could be accepted as first layer as it is common in ANNs and it is emphasized in their first indices;

O_{11} {= μ}_{A1} (x) {, O}_{12} {= μ}_{A2} (x) {, O}_{13} {= μ}_{A3} (x) {; O}_{14} {= μ}_{B1} (x) {, O}_{15} {= μ}_{B2} (x) {, O}_{16} {= μ}_{B3} (x);

These parameters can be accepted as premise parameters similar to Fuzzy Systems³⁷ or (IF) part of the ANFIS.

2’nd layer (product layer): In order to combine antecedent (IF) part of the rules, AND logical operator which is realized by a production function is employed. Outputs of the layers determine weights (w_i) of the related rules;

Rule 1: O₂₁ = w₁ = μ_A1 (x)* μ_B1 (x); Rule 2: O₂₂ = w₂ = μ_A1 (x)* μ_B2 (x);

Rule 3: O₂₃ = w₃ = μ_A1 (x)* μ_B3 (x); Rule 4: O₂₄ = w₄ = μ_A2 (x)* μ_B1 (x);

Rule 5: O₂₅ = w₅ = μ_A2 (x)* μ_B2 (x); Rule 6: O₂₆ = w₆ = μ_A2 (x)* μ_B3 (x);

Rule 7: O₂₇ = w₇ = μ_A3 (x)* μ_B1 (x); Rule 8: O₂₈ = w₈ = μ_A3 (x)* μ_B2 (x);

Rule 9: O₂₉ = w₉ = μ_A3 (x)* μ_B3 (x);

3’rd layer (normalized layer): This layer is used for normalization (N), that is weight of the related rule is divided into total weights.

{\bar{w}}_{1} = \frac{w_{1}}{\sum_{i = 1}^{9} w_{i}}

We may bring up the equation as;

{\bar{w}}_{1} = \frac{μ A 1 (x) * μ B 1 (x)}{μ A 1 (x) * μ B 1 (x) + μ A 1 (x) * μ B 2 (x) + μ A 1 (x) * μ B 3 (x) + μ A 2 (x) * μ B 1 (x) + μ A 2 (x) * μ B 2 (x) + μ A 2 (x) * μ B 3 (x) + μ A 3 (x) * μ B 1 (x) + μ A 3 (x) * μ B 2 (x) + μ A 3 (x) * μ B 3 (x)}

Similarly the rest of the normalizations are as follows;

{\bar{w}}_{2} = \frac{w_{2}}{\sum_{i = 1}^{9} w_{i}}, {\bar{w}}_{3} = \frac{w_{3}}{\sum_{i = 1}^{9} w_{i}}, {\bar{w}}_{4} = \frac{w_{4}}{\sum_{i = 1}^{9} w_{i}}, {\bar{w}}_{5} = \frac{w_{5}}{\sum_{i = 1}^{9} w_{i}},

{\bar{w}}_{6} = \frac{w_{6}}{\sum_{i = 1}^{9} w_{i}}, {\bar{w}}_{7} = \frac{w_{7}}{\sum_{i = 1}^{9} w_{i}}, {\bar{w}}_{8} = \frac{w_{8}}{\sum_{i = 1}^{9} w_{i}}, {\bar{w}}_{9} = \frac{w_{9}}{\sum_{i = 1}^{9} w_{i}}

4th Layer (defuzzy layer): The 4th layer includes and combines the consequence (THEN) parameters of the fuzzy rules and in this layer implication process are addressed.³⁸

z_{i} {=p}_{i} {*x+q}_{i} {*y+r}_{i}

Normalized weights of each rule imply the contribution degree of the related rule’s output¹⁷;

O_{4 i} = {\bar{w}}_{i} * z_{i}

i = 1.9 and O_4i refers the weighted output of each rule.

For example

O_{41} = {\bar{w}}_{1} * z_{1}

O 41 = \frac{μ A 1 (x) * μ B 1 (x)}{μ A 1 (x) * μ B 1 (x) + μ A 1 (x) * μ B 2 (x) + μ A 1 (x) * μ B 3 (x) + μ A 2 (x) * μ B 1 (x) + μ A 2 (x) * μ B 2 (x) + μ A 2 (x) * μ B 3 (x) + μ A 3 (x) * μ B 1 (x) + μ A 3 (x) * μ B 2 (x) + μ A 3 (x) * μ B 3 (x)} * z_{1}

O 41 = \frac{(μA 1 (x) * μ B 1 (x)) * (p 1 x + q 1 y + r 1)}{μ A 1 (x) * μ B 1 (x) + μ A 1 (x) * μ B 2 (x) + μ A 1 (x) * μ B 3 (x) + μ A 2 (x) * μ B 1 (x) + μ A 2 (x) * μ B 2 (x) + μ A 2 (x) * μ B 3 (x) + μ A 3 (x) * μ B 1 (x) + μ A 3 (x) * μ B 2 (x) + μ A 3 (x) * μ B 3 (x)}

5th Layer (output layer): This layer only aggregates the weighted outputs and obtains a scalar output value, in other words, deffuzzification result.

\begin{array}{l} z = O_{5} = \sum_{i = 1}^{9} O_{4 i} \\ {=O}_{41} {+O}_{42} {+O}_{43} {+O}_{44} {+O}_{45} {+ O}_{46} {+O}_{47} {+ O}_{48} {+ O}_{49} \end{array}

y = \frac{μ A 1 (x) * μ B 1 (x)}{μ A 1 (x) * μ B 1 (x) + μ A 1 (x) * μ B 2 (x) + μ A 1 (x) * μ B 3 (x) + μ A 2 (x) * μ B 1 (x) + μ A 2 (x) * μ B 2 (x) + μ A 2 (x) * μ B 3 (x) + μ A 3 (x) * μ B 1 (x) + μ A 3 (x) * μ B 2 (x) + μ A 3 (x) * μ B 3 (x)} * z_{1}

+ \frac{μ A 1 (x) * μ B 2 (x)}{μ A 1 (x) * μ B 1 (x) + μ A 1 (x) * μ B 2 (x) + μ A 1 (x) * μ B 3 (x) + μ A 2 (x) * μ B 1 (x) + μ A 2 (x) * μ B 2 (x) + μ A 2 (x) * μ B 3 (x) + μ A 3 (x) * μ B 1 (x) + μ A 3 (x) * μ B 2 (x) + μ A 3 (x) * μ B 3 (x)} * z_{2}

+ \frac{μ A 1 (x) * μ B 3 (x)}{μ A 1 (x) * μ B 1 (x) + μ A 1 (x) * μ B 2 (x) + μ A 1 (x) * μ B 3 (x) + μ A 2 (x) * μ B 1 (x) + μ A 2 (x) * μ B 2 (x) + μ A 2 (x) * μ B 3 (x) + μ A 3 (x) * μ B 1 (x) + μ A 3 (x) * μ B 2 (x) + μ A 3 (x) * μ B 3 (x)} * z_{3}

+ \frac{μ A 2 (x) * μ B 1 (x)}{μ A 1 (x) * μ B 1 (x) + μ A 1 (x) * μ B 2 (x) + μ A 1 (x) * μ B 3 (x) + μ A 2 (x) * μ B 1 (x) + μ A 2 (x) * μ B 2 (x) + μ A 2 (x) * μ B 3 (x) + μ A 3 (x) * μ B 1 (x) + μ A 3 (x) * μ B 2 (x) + μ A 3 (x) * μ B 3 (x)} * z_{4}

+ \frac{μ A 3 (x) * μ B 3 (x)}{μ A 1 (x) * μ B 1 (x) + μ A 1 (x) * μ B 2 (x) + μ A 1 (x) * μ B 3 (x) + μ A 2 (x) * μ B 1 (x) + μ A 2 (x) * μ B 2 (x) + μ A 2 (x) * μ B 3 (x) + μ A 3 (x) * μ B 1 (x) + μ A 3 (x) * μ B 2 (x) + μ A 3 (x) * μ B 3 (x)} * z_{9}

Forward calculations of ANFIS can be summarized with a flowchart (Figure 3).

Figure 3.

ANFIS forward algorithm.

ANFIS learning algorithm: Backward optimization calculations

Learning algorithm of ANFIS determines the optimum parameter values of FIS when a training set ${(x^{1}, y^{1}),…, (x^{k}, y^{k})}$ is given. The optimization is realized by minimization of error between the actual and desired output values. The parameters define the shape and/or position of the input and output membership functions (MF) on which several optimization methods could be applied³⁴.

Output membership functions can be updated as follows;

z_{i} (t + 1) = z_{i} (t) - η (O^{k} - y^{k}) {\bar{w}}_{i} (x^{k})

Results and discussion

ANFIS evaluation of adhesive wear behavior of GFRP composite materials

The GFRP composite samples are composed of Calcium carbonate (CaCO₃), Glass bead (GB), Alumina (Al), Polystrene (P) and Glass fiber (GF). Experimental tests indicate that percentage mixture rates (%) of these materials under various Load (L) and Speed (S) nonlinearly effects wear rate (WR) in the wear processes. That’s why it is hard to model wear rate (WR) estimations with analytical models. Proposed ANFIS model which is developed in MATLAB for prediction of these performance measures has 7 inputs and 1 output which are CaCO₃, P, GF, GB, Al, L, S and WR, respectively. Figure 4 shows Input-output illustration of the WR-ANFIS Prediction Structure.

Figure 4.

Input-output illustration of the WR-ANFIS prediction structure.

Twenty-four experimental wear test has been completed, 18 of which are used as training (Table 2) and the rest are used as validation data (Table 3). The GFRP composite materials D1, T1, T2, T3, T4 and T5 are six different mixtures of ingredients, whose ratios are given in the mentioned Tables. Materials (M) are subjected to adhesive wear test and each test is labeled with an Experiment Number (EN).

Table 2.

Training data.

Input data									Output data
M	EN	CaCO₃ (wt%)	P (wt.%)	GF (wt.%)	GB (wt.%)	Al (wt.%)	L (N)	S (rpm)	WR (mm³/Nm)*10⁻⁶
D1	1	30	0	40	10	0	10	100	700
	2	30	0	40	10	0	10	200	583
	3	30	0	40	10	0	20	100	929
T1	5	68	0	11	0	1	10	100	235
	6	68	0	11	0	1	10	200	237
	7	68	0	11	0	1	20	100	605
T2	9	60	8	11	0	1	10	100	34
	10	60	8	11	0	1	10	200	42
	11	60	8	11	0	1	20	100	684
T3	13	56	8	11	5	0	10	100	52
	14	56	8	11	5	0	10	200	35
	15	56	8	11	5	0	20	100	115
T4	17	63	0	11	5	1	10	100	139
	18	63	0	11	5	1	10	200	163
	19	63	0	11	5	1	20	100	154
T5	21	55	8	11	5	1	10	100	25
	22	55	8	11	5	1	10	200	29
	23	55	8	11	5	1	20	100	554

Table 3.

Testing data.

Input data									Output data
M	EN	CaCO₃ (wt%)	P (wt.%)	GF (wt.%)	GB (wt.%)	Al (wt.%)	L (N)	S (rpm)	WR (mm³/Nm)*10⁻⁶
D1	4	30	0	40	10	0	20	200	777
T1	8	68	0	11	0	1	20	200	446
T2	12	60	8	11	0	1	20	200	83
T3	16	56	8	11	5	0	20	200	41
T4	20	63	0	11	5	1	20	200	261
T5	24	55	8	11	5	1	20	200	490

Training process

In this study, ANFIS structure is generated with sub-clustering method where hybrid optimization method is applied. Error tolerance along the training stage is selected as 10⁻³ and maximum training epochs was 50. The structural information about the ANFIS model is given in Table 4.

Table 4.

Structure and parameters of WR-ANFIS prediction model.

Fuzzy inference system (FIS) type	Sugeno
Number of inputs	7
Number of outputs	1
Number of Rules	18
Number of Training Data	18
Number of Test Data	6
Operatorsused in Fuzzy AND (Conjuction of Antecent part of IF-THEN rules) Method	Minimum
Operators used in Fuzzy OR (Composition) Method	Probabilistic OR
Fuzzy Implication Method Operator	Minimum
Fuzzy Aggregation Method Operator	Maximum
Defuzzification Method	Weighted average of all rule outputs (Wtaver)
FIS Generation Method	Sub-Clustering
Error tolerance of the FIS Training Stage	10⁻³
Maximum epochs of the FIS Training Stage	50 iterations
Optimization Method of the FIS Training	Hybrid

Membership functions of the CaCO₃ variable for the trained ANFIS model is given as an example in Supplementary Figure A-1. Following the training stage, WR-ANFIS Model outputs matched well with the training data (Figure 5).

Figure 5.

Testing results for the trained WR-ANFIS prediction structure. o-training data, *ANFIS results.

Relation surfaces obtained from the trained ANFIS

Relation surfaces between output and inputs of the trained ANFIS Model are interpreted refer to each input pairs. Interactive effects of ingredients could be analysed and interpreted by relation surfaces of Model: Unlike glass fiber (GF) (Figure 6(b)), higher levels of CaCO₃ and polystrene (P) (Figure 6(a)) decrease the wear rate (WR).

Figure 6.

The relationship between wear rate (WR) and CaCO_3, P, GF. (a) CaCO₃ and polystrene (P). (b) CaCO₃ and glass fiber (GF).

Under %40 levels of CaCO₃, glass bead (GB) level is directly proportional to wear rate (WR). However, in the lack of GB, higher levels beyond %40 of CaCO₃ somewhat increases the WR. In this interwined region, GB is inversely proportional to WR (Figure 7(a)). In lower level of alumina (Al), CaCO₃ amount decreases the wear rate as usual under 200 levels. In higher concentration of alumina (Al), wear rate directly decreases to a relatively lower level (Figure 7(b)). But, if it is possible to use higher concentration of CaCO₃, WR could reduce to lower levels in the lack of alumina (Al).

Figure 7.

The relationship between wear rate (WR) and CaCO_3, GB, Al. (a) CaCO₃ and glass bead (GB). (b) CaCO₃ and alumina (Al).

On the other hand, wear rate (WR) is nonlinearly but almost directly proportional to load (L) where increasing CaCO₃ level palliates these effects (Figure 8(a)). Increasing speed (S) is inversely proportional to wear rate. Higher speeds and higher CaCO₃ levels result in minimum (WR)’s (Figure 8(b)).

Figure 8.

The relationship between wear rate (WR) and CaCO₃, load (L), speed (S). (a) CaCO₃ and load (L). (b) CaCO₃ and speed (S).

Speed (S) has a general reducing effect on wear rate (WR). But its’ effects can be analysed in details and can be interpreted under various concentrations. Higher polystyrene (P) concentrations reduce (WR) under higher speed, however contrariwise effect under lower speed (Figure 9(a)). Glass fiber (GF) concentrations over 30% have negative effect which could be noticed more under lower speed (Figure 9(b)).

Figure 9.

The relationship between wear rate (WR) and speed (S), P, GF. (a) Speed (S) and polystrene (P). (b) Speed (S) and glass fiber (GF).

Medium concentrations of glass bead (GB) (between 4%-8%) are satisfactory for wear rate (WR). But lower levels under 1% are ideal for speed (S) over 190 rpm (Figure 10(a)). Alumina (Al) concentration negatively affects wear rate (Figure 10(b)).

Figure 10.

The relationship between wear rate (WR) and speed (S), GB, Al. (a) Speed (S) and glass bead (GB). (b) Speed (S) and alumina (Al).

Both load (L) and speed (S) have directly proportional effect on wear rate (WR) (Figure 10(a)). As mentioned for speed, medium levels of glass bead concentration are satisfactory for wear under various load (L)’s. It could be reduced more under lower load (Figure 11(b)). Wear rate (WR) is minimum under higher polystyrene (P) and lower load (L). However, if load should be higher than 14 N, higher polystyrene concentrations result in inverse effect on wear rate. Lower levels of polystyrene could be acceptable under any load (Figure 12(a)). Higher polystyrene and glass bead (GB) together effect wear rate positively. Lack of polystyrene or lower concentrations of polystyrene increases the wear rate under higher glass bead rates and vice versa (Figure 12(b)).

Figure 11.

The relationship between wear rate (WR) and speed (S), load (L), glass bead (GB). (a) Speed (S) and load (L). (b) Load (L) and glass bead (GB).

Figure 12.

The relationship between wear rate (WR) and L, P, GB. (a) Load (L) and polystrene (P). (b) Polystrene (P) and glass bead (GB).

Minimum wear rate (WR) is obtained under lower load (L). If higher load is required, optimum wear rate could be provided under very low level, ideally at zero grade of alumina (Al) (Figure 13(a)). When the glass fiber (GF) concentration is under 25%; wear rate reaches to minimum value, and slightly increases refer to the glass bead (GB) concentrations over 3% and under 3%, respectively. Contrariwise wear rate values are obtained beyond higher glass fiber concentrations (Figure 13(b)).

Figure 13.

The relationship between wear rate (WR) and L, Al, GF, GB. (a) Load (L) and alumina (Al). (b) Glass fiber (GF) and glass bead (GB).

Some data could be tested by means of Rule Viewer application of Matlab ® FIS toolbox (Supplementary Figure A-2).

Testing stage of the trained model

Testing data given in Table 3 is used in validation of the trained ANFIS Model for the WR estimation (Table 5). Material D1 which used in the 4th experiment is estimated with the minimum relative error.

Table 5.

Testing results.

M	EN	Actual wear rate (WR) (mm³/Nm)*10⁻⁶	Estimated wear rate (WR) (mm³/Nm)*10⁻⁶	Relative Percentage error (%)
D1	4	777	748	3.732304
T1	8	446	397	10.98655
T2	12	83	96	−15.6627
T3	16	41	54	−31.7073
T4	20	261	217	16.85824
T5	24	490	582	−18.7755

Regression analysis of the estimation results is obtained by the equation of mean relative error (MRE), where numerator of the equation indicates the sum squared error (SSE) between actual (O_A) and estimated (O_E) output values and denominator represents the O_A (equation (12)).

MRE = \frac{\sum_{j = 1}^{N} (O_{A_{j}} - O_{E_{j}})}{O_{A_{j}}}

R² regression value between actual and estimation results are obtain a 0,964 correlation (Figure 14).

Figure 14.

Graphic of comparison between testing (actual) and estimation data.

Within the input-output ranges given for the ANFIS Model, the trained model is tested in a program loop (Supplementary Figure A-3) for all input combinations. Minimum wear values estimated by the trained model are given in Table 6.

Table 6.

Minimum wear rate values.

Results	CaCO₃ (wt%)	P (wt.%)	GF (wt.%)	GB (wt.%)	Al (wt.%)	L (N)	S (rpm)	WR (mm³/Nm)*10⁻⁶
ANFIS Estimation	49	0	11	10	0.8	10	100	25.0013
Experiment 21	55	8	11	5	1	10	100	25

It is obvious that the estimation result is a little bit higher than the results of the 21st experiment. However, FIS are universal approximators and they can interpolate within their ranges. WR-ANFIS estimation model extracts reasonable results. They can be tested for their out of range, but extrapolation results could not be trustable.

Conclusions

The aim of this study was to determine the optimum material content and working conditions in terms of wear resistance. Wear rate is an important outcome to attain higher productivity levels in the wear mechanisms. In this study, ANFIS based estimation model is developed in order to predict the wear rate appeared in the wear mechanisms of glass fiber reinforced polyester (GFRP) composite materials.

Minimum wear values are estimated by the trained model. The WR-ANFIS model extracted optimum concentrations and operating parameters to obtain the minimum wear rate. Due to the wear rate estimation model, optimum wear rate value is reached to 25.0013 (mm³/Nm)*10⁻⁶ at CaCO₃, polystyrene (P), glass fiber (GF), glass bead (GB), alumina (Al), load (L) and speed (S) values of 49%, 0%, 11%, 10%, 0.8%, 10 N and 100 rpm respectively. WR-ANFIS estimation model extracts reasonable results. A high estimation capability (R² = 0.964) has been achieved using ANFIS Model.

Wear rate depends on different wear mechanisms and ingredient concentration parameters. ANFIS models propose a reasonable estimation results and relation surfaces which illustrates general behavior of the nested effects and allow us to interpret and inferdecisions on itself.

Supplemental material

sj-tif-1-jep-10.1177_00952443211020793 – Supplemental Material for Estimation of adhesive wear behavior of the glass fiber reinforced polyester composite materials using ANFIS model

Supplemental Material, sj-tif-1-jep-10.1177_00952443211020793 for Estimation of adhesive wear behavior of the glass fiber reinforced polyester composite materials using ANFIS model by Serhat Yilmaz, Recep Ilhan and Erol Feyzullahoğlu in Journal of Elastomers & Plastics

Supplemental material

sj-tif-2-jep-10.1177_00952443211020793 – Supplemental Material for Estimation of adhesive wear behavior of the glass fiber reinforced polyester composite materials using ANFIS model

Supplemental Material, sj-tif-2-jep-10.1177_00952443211020793 for Estimation of adhesive wear behavior of the glass fiber reinforced polyester composite materials using ANFIS model by Serhat Yilmaz, Recep Ilhan and Erol Feyzullahoğlu in Journal of Elastomers & Plastics

Supplemental material

sj-tif-3-jep-10.1177_00952443211020793 – Supplemental Material for Estimation of adhesive wear behavior of the glass fiber reinforced polyester composite materials using ANFIS model

Supplemental Material, sj-tif-3-jep-10.1177_00952443211020793 for Estimation of adhesive wear behavior of the glass fiber reinforced polyester composite materials using ANFIS model by Serhat Yilmaz, Recep Ilhan and Erol Feyzullahoğlu in Journal of Elastomers & Plastics

Footnotes

Acknowledgements

The samples are supplied from “Sami Tongün Glass Fiber Polyester Products, Kocaeli/Turkey”. The authors thank for the materials and cooperation of Sami Tongün Glass Fiber Polyester Products.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Supplemental material

Supplemental material for this article is available online.

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