Artificial Neural Network and Response Surface Methodology Based Analysis on Solid Particle Erosion Behavior of Polymer Matrix Composites

Polymer-based fibrous composites are gaining popularity in marine and sports industries because of their prominent features like easy to process, better strength to weight ratio, durability and cost-effectiveness. Still, erosive behavior of composites under cyclic abrasive impact is a significant concern for the research fraternity. In this paper, the S type woven glass fibers reinforced polymer matrix composites (PMCs) are used to analyze the bonding behavior of reinforcement and matrix against the natural abrasive slurry. The response surface methodology is adopted to analyze the effect of various erosion parameters on the erosion resistance. The slurry pressure, impingement angle and nozzle diameter, were used as erosion parameters whereas erosion loss, i.e., weight loss during an erosion phenomenon was considered as a response parameter. The artificial neural network model was used to validate the attained outcomes for an optimum solution. The comparative analysis of response surface methodology (RSM) and artificial neural network (ANN) models shows good agreement with the erosion behavior of glass fiber reinforced polymer matrix composites.


Introduction
The demand for polymer matrix composites (PMCs) has been increased significantly in recent years for industrial and household's applications [1][2][3][4]. The lightweight, better strength and economically affordability made them highly recommended material for the shed in coastal as well as in desert areas. However, the constant abrasive attack in the form of storm and slurry mixed winds causes surface degradation [5,6]. The continuous bombardments of these particles weaken the bonding strength, which causes material failure. This constant bombardment degrades the surface and reduces the material's life [7]. The erosion on the surface initiates with imprints of minute cracks induced due to stress caused by continuous slurry impact. The components made up of PMCs in aircraft's

Materials and Methods
Erosion of the composite surface is a complex material phenomenon in which several controlled/uncontrolled parameters collectively affect output quality characteristics. In this paper, statistical analysis of different process parameters for wear behavior of the hybrid polymer matrix composite was studied using the response surface methodology [29]. The box Behnken design based experimental plan was used to study the optimal parametric combination. The experimentation was performed on the developed solid particle erosion test setup (Figure 1) based on the ASTM G76 standard. The polymer matrix composite reinforced with S glass fibers was used as a workpiece material. The river sand particles were mixed with air to bombard on the workpiece as abrasive slurry. The SEM of the cut sectional view of the fabricated composite is shown in Figure 2. The figure clearly shows the different layers of fibers bonded with the polymer matrix. The morphology of the abrasive river sand particles is shown in Figure 3. The magnified images of the sand particles depict that particles possess tapered and sharp edges, which will affect the erosion phenomenon. To keep an eye on erosion behavior, the electronics weighing machine with a least count of 0.0001 g was used to record weight loss. To make the data analysis simple, the ranges were coded based on experimental runs. The point of optimality was chosen at 0 levels. The coded values were determined as follows [30]:

Response Surface Methodology
Response surface methodology (RSM) explores the association among numerous process parameters with the response parameter. The observational model is generated by using f numerical and geometric techniques. The generated model is used to improve the response reaction, which is prejudiced by several input parameters. In this paper, the Box-Behnken design was adopted for Here N 1 , and N o are values at level 1, and level 0 whereas N K is actual parametric value to level interest.
The observed experimental results are shown in Table 2. A developed mathematical model based on RSM for correlation of erosion in terms of coded parameters is as follows:

Response Surface Methodology
Response surface methodology (RSM) explores the association among numerous process parameters with the response parameter. The observational model is generated by using f numerical and geometric techniques. The generated model is used to improve the response reaction, which is prejudiced by several input parameters. In this paper, the Box-Behnken design was adopted for Materials 2020, 13, 1381 5 of 13 experimental planning. During RSM, a quantifiable system of association among input parameters and response parameter could be stated as Here Y is anticipated response and Fis response function. For the analysis, a second-order polynomial regression model, which is called a quadratic model, can be written as The term b 0 and b i are second-order regression coefficients and b ii and b ij represents a quadratic effect. K represents several machining parameters and x i and x j represents terms, which deal with the effect of machining parameters.

Artificial Neural Network
Artificial neural network (ANN) model is an algebraic model that spontaneously approximates the ability of conventional neural systems. A multilayer perceptron (MLP) was generated in through three input neurons viz. slurry pressure, nozzle diameter and impingement angle, neurons as hidden layers, and target neuron representing the erosion loss. The eccentricity of forecasts from investigational results was reduced by neurons essential in the hidden layer and investigated by a trial. A minimum of ten neurons was obligatory to construct the most recent model using the data accessible, and the development of new neurons presented the probability of over-fitting the model. A cumulative of 90% of investigative consequences was used to formulate the model, with the remaining outcomes, divided justifiably between model consent and testing. The procedure of deciphering fitting problems requires a neural network to plot between input statistics and a set of numeric targets ( Figure 4).
Here Y is anticipated response and ɸ is response function. For the analysis, a second-order polynomial regression model, which is called a quadratic model, can be written as  During the training phase, the process starts by providing input (data) into the input nodes of the neural network. Then, the feed will be forwarded to the present output on the output nodes of the network. If a similar input is feed in the network, the small error will be generated. In every attempt of training data, the overall error of the network can be measured. The training phase will complete after attaining the best possible solution. The accuracy of the prediction can be influenced by the ANN parameter, i.e., the number of hidden layers. The single hidden layer can estimate the function, which comprises of continuous mapping from one finite space to the adjacent whereas multiple hidden layers signify the arbitrary decision boundary to arbitrary accuracy with a rational activation function. Additionally, multiple hidden layers can estimate any suave mapping to any precision. If there is no hidden layer present, the network will show a discrete linear function.

Parametric Evaluation through RSM
The ANOVA test was conducted to validate the suitability of developed models for creating a link between the erosion parameters and response. The analysis of variance for erosion is depicted in Table 3. From the ANOVA table, it is clear that the impingement angle was the most significant erosion parameter for the solid particle jet erosion process. The combined effect of machining parameters on erosion is shown in Figure 5a-c. Figure 5a shows the influence of slurry pressure and nozzle diameter on the erosion rate at a constant impingement angle of 60 • . The interaction of parameters predicts that at a constant impingement angle of 60 • , the erosion was highest with a slurry pressure of 75 Psi and a nozzle diameter of 2.5 mm. The combined effect of the nozzle diameter and impingement angle at constant slurry pressure of 75 Psi is shown in Figure 5b. The results predict that erosion increased with an increase in the impingement angle from 30 to 60 • but started decreasing in the next level. During this phase, the nozzle diameter had the least effect on erosion loss. Figure 5c shows the interaction effect of slurry pressure and impingement angle on erosion at a constant nozzle diameter of 2.5 mm. The surface plot indicates that a medium level of impingement angle with maximum slurry pressure produced higher erosion over the composite surface.

Modeling Through ANN
The model is incited by the observance that can acquire within the prospect of a trainer. During modeling, the trainer specifies the precise responses to the contributing parameters. The neural model can equally gain without a trainer, reliant on the criteria of self-association. The neural model illustration is principally established on technical models. The model can be reflected as a model of neurons arranged in limited layers to be explicit the contributing parameters, hidden neurons and response. This methodology has arisen as an innovative and extensive model, which can be regulated to assess any mapping with enough perceptiveness of layers and number of neurons. Table 4 shows the result obtained from the planning of the model. Mean squared error (MSE) characterizes the mediocre squared divergence amid response and targets. The lesser approximations of MSE are healthier, and zero shows no error. Regression (R) values express the linking amid response and goals. An R-value of 1 indicates a sensible bond, and 0 indicates an uneven association. Although, the approximations of MSE and R are nearby zero and one individually. This suggests the curve fitting was exact in the control. The predictable network model was planned equitably, and its

Modeling Through ANN
The model is incited by the observance that can acquire within the prospect of a trainer. During modeling, the trainer specifies the precise responses to the contributing parameters. The neural model can equally gain without a trainer, reliant on the criteria of self-association. The neural model illustration is principally established on technical models. The model can be reflected as a model of neurons arranged in limited layers to be explicit the contributing parameters, hidden neurons and response. This methodology has arisen as an innovative and extensive model, which can be regulated to assess any mapping with enough perceptiveness of layers and number of neurons. Table 4 shows the result obtained from the planning of the model. Mean squared error (MSE) characterizes the mediocre squared divergence amid response and targets. The lesser approximations of MSE are healthier, and zero shows no error. Regression (R) values express the linking amid response and goals. An R-value of 1 indicates a sensible bond, and 0 indicates an uneven association. Although, the approximations of MSE and R are nearby zero and one individually. This suggests the curve fitting was exact in the control. The predictable network model was planned equitably, and its presentation was scheduled to validate if any alteration to be prepared for the training practice. Figure 6 shows the performance curve for the developed models. The models show the best validation point occurred at the second iteration. Figure 7 determines the generated regression plots for the testing, training and validation procedure. The obtained result shows the linkage between target and response from the model. Figure 8 exhibits the error histogram for the organized neural model. presentation was scheduled to validate if any alteration to be prepared for the training practice. Figure 6 shows the performance curve for the developed models. The models show the best validation point occurred at the second iteration. Figure 7 determines the generated regression plots for the testing, training and validation procedure. The obtained result shows the linkage between target and response from the model. Figure 8 exhibits the error histogram for the organized neural model.

Discussion
The overall analysis shows that the impingement angle of striking the slurry influenced the erosion process more significantly than slurry pressure and nozzle diameter. The available trends show that the present composite material could be classified in the semi ductile category because

Discussion
The overall analysis shows that the impingement angle of striking the slurry influenced the erosion process more significantly than slurry pressure and nozzle diameter. The available trends show that the present composite material could be classified in the semi ductile category because these materials show the highest erosion in the range of 45-60 • for the impingement angle [31]. Additionally, the essential factor in controlling the erosion behavior is the nature of the erodent particle. The irregular shape and size of erodent particles induce high erosion in polymer matrix composites [32]. The form of striking erosive particles profoundly influences the nature of deformation of the surface. The round edge particles induce plastic deformation, whereas sharp and hard particles exhibit brittle deformation of the surface [33]. The state of the composite surface at a variable impingement angle is shown in Figure 9a-c. At the impingement angle of 30 • , the abrasive slurry chipped off and tore down the composite surface, which made glass fibers visible as shown in Figure 9a. The slurry impact somehow degraded the upper layer, but the strong interfacial bond strength kept the fibers and matrix closely bonded. However, with the change in the impingement angle to 60 • , the degradation rate of the primary layer of matrix increased and brought reinforcement into direct contact of the abrasive slurry. The exposed reinforcement aligned in one direction and resulted in high erosion loss. The upper surface damage at the impingement angle of 60 • is visible in Figure 9b. The further increase in the impingement angle to 90 • decreases the horizontal component [34]. This decrease in the horizontal component decreased the cutting rate of fibers and matrix as compared to erosion at 60º because the increased vertical composite produced a harrier surface, which significantly reduced the erosion rate (Figure 9c). Although few broken fibers and matrix cracks were visible over the surface, still the matrix was uniformly bonded with fiber reinforcement. The validation and test outcomes additionally demonstrated the R-value that was more prominent than 0.90. The comparative analysis of the test and the anticipated value of erosion are shown in Table 5. The obtained results for erosion shows 0.043% deviation concerning results obtained from RSM ( Figure 10). The attained conclusions designated a prodigious pact between neural system anticipation and test validation standards. The validation and test outcomes additionally demonstrated the R-value that was more prominent than 0.90. The comparative analysis of the test and the anticipated value of erosion are shown in Table 5. The obtained results for erosion shows 0.043% deviation concerning results obtained from RSM ( Figure 10). The attained conclusions designated a prodigious pact between neural system anticipation and test validation standards.  The validation and test outcomes additionally demonstrated the R-value that was more prominent than 0.90. The comparative analysis of the test and the anticipated value of erosion are shown in Table 5. The obtained results for erosion shows 0.043% deviation concerning results obtained from RSM ( Figure 10). The attained conclusions designated a prodigious pact between neural system anticipation and test validation standards.

Conclusions
The following conclusions were drawn from the present study:

Conclusions
The following conclusions were drawn from the present study: 1.
The erosion during the solid particle impact is deeply affected by the impingement angle. The maximum erosion occurred at an angle of 60 • , which means the composite lay in the category of semi ductile materials.

2.
From the ANOVA table for erosion, the most significant and influential parameter was found to be the impingement angle. Additionally, the generated quadratic models were suitably fitted with investigational results. 3.
The SEM analysis of the river sand particles shows the irregular and sharp conical edges, which were responsible for the high erosion rate. 4.
The SEM analysis of composite surface shows that the impingement angle of 60 • degraded the upper layer of the composite very finely and exposed the fibers, which caused an excess material loss in comparison to a 30 • and 90 • impingement angle. 5.
MATLAB's neural network fitting app was used for generating a network model, which produced good comparative results by using hidden layers and neurons. The developed model showed 0.43% deviation with the results obtained from RSM based model. 6.
The multiple hidden layers signified an arbitrary decision boundary to arbitrary accuracy with rational activation function and provided precise result with minimal deviation in comparison to the RSM model. 7.
The comparative analysis showed that the ANN model could be used proficiently for the validation of single response optimized results obtained during solid particle erosion of polymer matrix composites.