Artificial neural network prediction and grey relational grade optimisation of friction stir processing

Abstract The study predicts friction stir process (FSP) parameters using an artificial neural network (ANN) model. A design of experiment (DoE) approach is used to conduct experiments on FSP and to evaluate the best operating parameters of FSP. ANN uses 30 neurons, 1 hidden layer, and an input and output layer in the Matlab® environment. ANN predicts the output parameters with R values of 0.999, 0.995, and 0.992 for training, validation, and test datasets, respectively, while the overall R-value is 0.997. GRA is used to optimize and rank the parameters of the processes and revealed that the rotational tool speed should be 1180 rpm, traverse feed rate 38 mm/min, and tool tilt angle 1° for best results. The optimized values obtained are 380 MPa, 3.8 µm, 138 HV, and 14% for tensile strength, grain size, microhardness, and elongation, respectively. According to the analysis of variance (ANOVA) and grey relational analysis, the order of influencing parameters on output factors was rotational speed (80%), followed by transverse feed (19%) and tool tilt angle (1%). An ANN is further used to predict using the two most significant parameters—rotational speed and traverse feed. The modified ANN has nearly the same R values as the original ANN. Thus modified ANN may be used for prediction.


ABOUT THE AUTHORS
Wable A D is a research scholar in the Department of Production and Industrial Engineering, College of Engineering Pune.He received his Bachelor's degree from Dr. Babasaheb Ambedkar Marathwada University, Aurangabad; his Master's degree from Veermata Jijabai Technological Institute; and a Ph.D. from College of Engineering Pune, Savitribai Phule Pune University, Pune, Maharashtra, India.He has 2 years of Industrial experience and 8 years of teaching experience.His research interest includes Friction stir processing.Patil S B is a Professor in the Department of Mechanical Engineering, College of Engineering Pune.He has over 25 years of teaching and research experience.His research interests include advanced manufacturing processes and optimization techniques.He received his Bachelor's degree in Production Engineering from Shyamlal College of Engineering, Udgir; his Master's degree in Production -Industrial Engineering and Management from Veermata Jijabai Technological Institute; and his Ph.D. from Swami Ramanand Teerth Marathwada University Nanded, India.To his credit, he has more than 10 publications in reputed journals.Pardeshi S S is a Professor in the Department of Mechanical Engineering, College of Engineering Pune.He has over 15 years of teaching and research experience.His research interests include Micro Systems Engineering Compliant Mechanisms.He received his Bachelor's degree in Mechanical Engineering from Sanjivani College of Engineering, Kopargaon, his Master's degree in Production Engineering, and his Ph.D. from College of Engineering, Pune.To his credit, he has more than 20 publications in reputed journals.

Introduction
The technology for processing materials is as old as civilization itself.In the 19th century, England revolutionized machine automation for forming, shaping, and cutting.Materials processing technologies, techniques, and machinery have advanced significantly (Sun & Apelian, 2009).Material processing was introduced to enhance material qualities for a specific application.The material selection with specified qualities is a critical parameter in many manufacturing industries, including aircraft, automobiles, and watercraft (McNelley, 2011).Aluminum is well-known for being lightweight and corrosion-resistant.These characteristics have drawn attention to this material, causing it to become the ideal material for airplane structures, ship structures, and automotive components.Another advantage of choosing aluminum is that its lightweight helps to lower power usage (Kumar et al., 2012).
Deep learning developed from ANN, which is a type of machine learning.Most deep learning methods imply the neural network architecture, which is why they are sometimes referred to as deep neural networks.Deep learning uses numerous nonlinear processing layers for supervised or unsupervised learning.It attempts to learn from hierarchical data descriptions.Deep learning is used in various industries, from automated machines to medical equipment (Deng, 2014).Wuest, Weimer, and Irgens distinguished the supervised and unsupervised ML algorithms & Thoben (Wuest et al., 2016).Because most manufacturing applications supply labeled data, SVM has been proven to be a good fit for most of them.In supervised machine learning, SVMs are the most often utilized algorithm in manufacturing.ML is a formidable tool, and its importance will grow in the coming days.Face recognition, image processing, manufacturing, and medical applications are just a few commercially available research topics for machine learning.
Most researchers have concentrated on the mechanical and metallurgical features of the FSW joints.In contrast, a few have attempted to assess the performance of FSW on various materials using various modeling and optimization techniques.Using artificial neural network modeling, Okuyucu et al. (2007) studied the mechanical properties of FS-welded joints (ANN).Rajakumar and Alasubramanian (2012) used response surface methodology (RSM) for optimizing the process parameter of FSW.To identify the association between the input and output process parameters, Shojaeefard et al. (2015) used ANN modeling.For combining different welding metal plates, Na et al. (2008) used tungsten arc welding.They employed the SVR model to predict joint residual stresses.Elsheikh et al. (2019) presented a systematic review of ANN applications to predict the performance of solar energy devices for various applications.Authors have observed that ANN does not need complicated mathematics and fewer experimentations.Abu Shanab et al. (2021) have introduced AI-based techniques for predictive modeling of FSW using dissimilar materials like ABS and PC sheets.A hunger game search algorithm is used to optimize and correlate the joint properties such as tensile strength and efficiency of the joint.Authors have observed that the HGS algorithm yields superior results to the sine cosine algorithm.Khoshaim et al. (2021) have developed a multilayer perceptron's model optimized by the grey wolf algorithm to improve the mechanical properties and microstructure of AA2024 Al alloy.Authors have investigated the effect of multi-pass FSP reinforced with alumina nanoparticles.Authors have observed greater accuracy in the case of the developed model compared to the standalone model.The conclusion is that these models are highly accurate in predicting experiment outcomes.According to another researcher, Wang et al. (2008), SVM more precisely classifies the defect and non-defective aspects of the weld.Pal and Deswal (2010) adopted a gaussian process regression (GPR) technique to anticipate waterengineering difficulties.In addition, to forecast the performance of manufacturing processes SVM and GPR, ANN models were frequently employed (Manvatkar et al., 2012;Verma & Misra, 2017;Yousif et al., 2008).AA7075 (Magnesium-Zinc alloy) is commonly utilized in aircraft applications due to its high specific strength, hardness, and corrosion resistance at high temperatures (Yelamasetti et al., 2021).The primary alloying element in AA7075 is zinc.It has high strength, toughness, fatigue strength, and corrosion resistance.However, due to the microsegregation, AA7075 material undergoes embrittlement, reducing ductility significantly.AA7075-T6 is an advanced version of aluminum alloy, which is obtained by the tempering process.The yielding and ultimate tensile strength of AA7075-T6 is high compared to AA7075 due to the fine and arrangement of the grained structure.
According to Aydin et al., the Taguchi technique is a very successful tool for process optimization under a restricted number of experimental runs (Aydin et al., 2010).The use of the Grey-based Taguchi approach significantly enhanced the tensile strength and elongation of welded AA1050-H22 aluminum alloy.Vijayan et al. 92010) investigated the optimization of process parameters in the FSW of aluminum alloy AA5083 using multiple responses and grey relational analysis.They aimed to determine the optimum levels of process parameters that would give the greatest tensile strength while using the least amount of energy.
2022) developed a correlation to predict input and output responses using FSP/Al2O3 nanoparticles.The developed model shows that the nanoparticle Al2O3 and FSP passes were the dominant parameters to improve the mechanical properties of the multi-pass FSP/Al2O3, where mechanical properties were observed as nanoparticle size increased.Husain and Mishra (2021) also fabricate SiC nanoparticles in AA 6082-T6by FSP and find enhancement in tensile strength and microhardness at the fifth pass of FSP.Further authors (Mehdi & Mishra, 2021a) defined that agglomeration of SiC particles decreases with increases in the number of FSP pass.
Mehdi et al. used the RSM model in FSW.They found that rotational tool speed and welding speed are dominating parameters affecting material tensile strength and microhardness (Salah et al., 2022).Mehdi et al. derived the relationship of percentage elongation, tensile strength, residual stress, and microhardness of the TIG + FSP-welded joint of AA6061 and AA7075.Authors have used a confidence level of 95% and observed that the tool's tilt angle and rotational speed are the significant parameters that affect the mechanical properties of aluminum alloys.In this analysis, the authors have derived process parameters for the optimum output result (Mehdi & Mishra, 2020).Hashmi et al. reduced the welding defects such as microvoids, porosity, coarse grain structure, and solidification defects by applying FSP after TIG welding, reducing the grain size and enhancing the tensile properties (Hashmi et al., 2022).Mehdi and Mishra observed higher tensile strength improvement of 78.57% and 75.89% in the TIG + FSP-welded sample compared with TIGwelded joints (Mehdi & Mishra, 2021b, 2021c).
Mehdi analyzed the mechanical properties of the TIG + FSP-welded joint.They developed a computational fluid dynamics model using the numerical model to predict the temperature distribution and material flow during TIG + FSP of dissimilar aluminum alloys AA6061 and AA7075 by ANSYS fluent software.The expected peak values at the weld temperature region are calculated.The maximum temperature and heat flux are observed at a tool rotation at 1300 rpm (Husain & Mishra, 2020).AA7075-T6 seems to have moderate mechanical properties like ultimate tensile strength and higher hardness.As a result, the material cannot form an L-shaped or V-shaped channel.The material may fail after bending, or the spring back effect may be detected.Ultimate tensile strength and ductility should be increased at the angle formation location.Friction stir processing can help to improve ultimate tensile strength and ductility.Friction stir processing is used to incorporate the microstructure and mechanical properties of the AA7075-T6.Periasamy et al. (2019).FSP, as shown in Figure 1, can strengthen a material's ultimate tensile strength and ductility at a specific location.In FSP, a single piece of material is placed into a revolving tool with a pin and the shoulder.Due to the rotating action of the tool, friction generates between the pin and shoulder surface with a base material.Because of the friction, enough heat is added to soften the material where the pin is entered.Due to the rotation of the pin, the material nearby to the pin undergoes plastic deformation, which causes grain refinement.This grain refinement will enhance the material's mechanical properties like ultimate tensile strength, hardness, and ductility (Montgomery, 2017).Some experiments are performed on the materials by considering the effect of input parameters on the output parameters.A set of several trails to be performed on the material is evaluated using Design of Experimentation (DOE; Montgomery, 2017) techniques.The effect of input parameters on output parameters is determined using the DOE method.An optimum parameter is identified based on the results of a set of experimental tests.The input parameters for this operation are rotational speed, traverse feed, and tilt angle.Ultimate tensile strength, hardness, ductility, and grain size are the output parameters.
Four output parameters are selected, such as ultimate tensile strength, hardness, ductility, and grain size, as AA7075-T6 is a hard material.Hence, while performing FSP on AA7075-T6 aluminum alloy, the material's ultimate tensile strength, ductility, and grain size should be increased, and hardness should be decreased.As the output parameters conflict, a multi-attribute decisionmaking method, i.e., grey relation analysis (GRA) (Girish et al., 2019), is suitable for solving this problem.
The work aims to find the optimum parameters for the FSP of AA7075-T6, such as ultimate tensile strength, ductility, hardness, and grain size.Gray relational analysis is used to obtain these ideal parameters.The objectives of this paper are as follows: • To enhance and evaluate the mechanical properties of AA7075-T6 by performing FSP.
• To implement ANN for prediction.
• To find the optimum set of parameters to improve mechanical properties by multi-attribute decision-making method.
• To obtain significant parameters of FSP by ANOVA.
In this paper, L 27 , the orthogonal array is used for experimental purposes.An ANN-based approach predicts the FSP parameters from the experimental data sets.Further, ANOVA technique is used to find the most significant parameter, and the GRA approach is used to determine the optimal parameters of the FSP process.The developed ANN model again predicted the most considerable parameter obtained using the ANOVA technique.

Experimental design for design of experiments
A statistical method known as DOEs (Elsheikh, Abd Elaziz et al., 2021, 2022;Wable & Patil, 2021) is used to find the most appropriate input parameters.This statistical tool aids in identifying the number of experiments required to attain the goal in the shortest amount of time and effort.The Orthogonal Arrays (OA) are used to determine various levels of input parameters.To assess the influence of 13 different parameters, each having three levels, we must use the L 27 Orthogonal Array.Table 1 presents the layout of the L 27 (3 13 ) Orthogonal Array.In Table 1, the value "−1" means Low level.
Value "0" means medium level, and value "1" indicates a higher level of input variables.
This research considers three input variables, each having three levels.An L 27 orthogonal array is used to carry out the investigation.

Artificial Neural Networks (ANN)
usually divided into sets, with one set used to build and train a network.ANN determines optimal weights during the learning phase.The remaining data set is utilized to validate the ANN and for prediction purposes after it has been trained and simulated.ANN improves the design process because of its prediction power (El-Gohary et al., 2011;Elsheikh, Katekar et al., 2021;Elsheikh, Panchal et al., 2021;Kalaivani et al., 2016;Khalil et al., 2013;Marconcini et al., 2011;Moustafa et al., 2022;H et al., 2021;Nagarkar et al., 2019;Sahu, 2012;Vignesh & Padmanaban, 2018).

Method of normalization-grey relational analysis
Grey relational analysis (GRA) is useful to correlate the input variables with the output variables.
Each input parameter has its significance on the output parameters.As the input variables have different units so, before processing the data, the normalization of all parameters is calculated (Elsheikh, Muthuramalingam et al., 2022;Elsheikh, Shehabeldeen et al., 2021).Step-1: Data pre-processing In this step, the data are normalized to a comparable sequence, so that all the units of different output parameters will be the same.This step converts original data to a similar arrangement depending on the various objectives.
The following formula is used to determine a larger value or a better value: The following formula is used to determine a smaller value as a better value: The following formula is used to determine a specific target value as a better value: i ðkÞ À OBj fmaximum y 0 i ðkÞ À OB; OB À minimum y 0 i ðkÞg where OB means specific target value.
To normalize the sequence of original values, the following formula is used. where, Step 2: Steps to calculate Grey relational coefficient A Grey relational coefficient is calculated by using the pre-processed sequences as follows: Step 3: Steps to calculate a coefficient of Grey relation A Grey relational grade (GRG) is calculated by taking the weighted sum of all Grey relational coefficients.It is defined as follows: The GRG is the relationship between the reference sequence values and comparability sequence values.If the reference sequence and comparability sequence values are identical, then the value of GRG is equal to one.The GRG shows the impact of reference sequence values on the comparability sequence values.Hence, if one comparability sequence value is more essential to the reference sequence value than other sequence values, then the GRG for that comparability sequence value and the reference sequence value will be higher than the GRG value for the other GRG value.Thus, the Grey relational method is used to determine the correlation between reference sequence values and comparability sequence values by measuring the absolute magnitude of data difference values between them.
A coefficient of grey relation is calculated after data pre-processing is carried out with the help of pre-processed sequence.The coefficient of grey relation shows the relationship between the ideal result value and the actual normalized experimental result value.The coefficient of grey relation is calculated as follows: where Δ 0i k ð Þ is the deviation of sequence value from the reference sequence value y � 0 k ð Þ and the comparability sequence value is (1) Now, F-ratio (F), SS', and percentage contribution (P) of non-pooled parameters and pooled error are calculated.This shows the contribution of every input parameter value to the output parameters value.

Data analysis with analysis of variance tool (ANOVA)
ANOVA is a statistical tool to interpret the data collected through experimentations.The method finds the significant parameter with the highest contribution to the output.This method helps determine the impact of multiple variables on the output.
The steps of ANOVA are given below: (1) The output data are tabulated in the number of responses.Depending on the nature of the objectives to be maximized, minimized, or nominal, the ratio of Signal to Noise (S/N) is calculated.
These formulas are listed below: Then, an orthogonal array with interaction matching the input data is selected from an available standard list.This array contains both level values of input variables as well as their interactions.
(2) Then calculate the sum of all the squares (SS) and degrees of freedom (DOF) of the variable and its interactions.
After calculating these terms, a total of both is calculated by simply adding the all-calculated values of both SS and DOF.
SST ¼ SSA þ SSBþ . . . . . . . . .: ( (3) After this, variance (V) and error (e) is calculated.The error (e) is calculated by adding the SS value of the columns to which no other parameter or interaction is assigned.
Pooling is a method by which the parameters or interactions, which do not have a greater influence on the output of the process, are pooled with the error value, and their SS are not considered for further calculations alone.After calculating the error value, the pooled error [e-(pooled)] value is calculated, which is added to the final result table, not the error.Then, the variance of e-(pooled) is calculated, termed Ve Ve ¼ SS=DOF: (15)

Experimental analysis
The DOE technique is used to conduct an experimental design.Rotational speed, traverse feed, and tilt angle, all these three parameters are considered input parameters.Table 2 shows three levels of all input parameters, which are selected.Ultimate tensile strength, hardness, ductility, and grain size are the output parameters.
An experimental analysis is conducted on aluminum alloy AA7075-T6.A rectangular plate of 6 mm is used to carry out friction stir processing.The chemical composition of the plate is shown in Table 3.
For performing the FSP operation, a threaded pin profile, as shown in Figure 3, which is made of non-consumable H-13 steel, is used.The shoulder diameter is 20 mm, the probe length is 5.8 mm, and the probe diameter is 3 mm with a thread pitch of 1 mm.
A single-pass FSP is carried out from one plate end to another.From this plate, a tensile test specimen, as shown in Figure 4, is prepared as per the American Society for Testing of Materials (ASTM-E8) standard.
The test specimen is mounted on UTM to determine UTS and % elongation.Also, the hardness and grain size of the specimen are observed and noted.
Energy-Dispersive X-Ray Spectroscopy (EDS) defines the chemical composition measured at the nugget zone and corresponding peaks shown in Figure 5(a,b).Elements can be seen in the welldistributed and synthesized structure in the EDS spectrum.Details of EDX spectra of the electrospun values are measured in atomic and weight%, as listed in Figure 5(b).
The Nugget zone is evaluated by SEM analysis of the cracked surface of the tensile samples to find the failure mode under uniaxial force.The base material BM fracture surface, shown in Figure 7(a).has a significant number of cleavage facets and only a small number of dimples, which are often signs of brittle-dominated fracture.The specimen's fractured surface, which was  processed at tool rotational speed 1180 rpm, traverse speed of 38 mm/min, and tool tilt angle of 1°, reveals a few more dimples of smaller sizes.After the FSP, the grain size is reduced, and precipitates of greater sizes are seen along the grain boundary region.The failure is caused by microvoids that aggregated after secondary precipitates in the grain boundary region fractured.
Due to decreasing heat input, the size of the second-phase particles reduced as traversal speed increased.The fractography in Figure 6(b) exhibits several dimples of varying sizes.This is characterized by the second-phase particles' less coarsening and refined grain size (Hashmi, Mehdi, Mabuwa et al., 2022;Hashmi, Mehdi, Mishra et al., 2022;Salah et al., 2022).It is seen that none of the FSP samples exhibit any cleavage-type facets or significant cracks.This shows that the brittledominated failure in the BM changes to an appearing ductile fracture for the FSP samples.
The results of the 27 test specimens are obtained and presented in Table 4. Figure 7(a,b) represents the microstructure before and after processing.

ANN analysis
The Nf tool solves static fitting problems with a standard two-layer feed-forward neural network trained with the Levenberg-Marquardt (LM) method.Despite the enormous data collection, training is done automatically with a scaled conjugate gradient, and performance is assessed using MSE and regression analysis.neurons are enhanced when the network does not perform properly after training.The training stops automatically when generalization stops improving, as shown by an increase in the mean square error of the validation data samples.Due to variable initialization of connection weights and different initial conditions, training several times yields diverse results.The mean squared error is the average difference between normalized outputs and targets; the zero value indicates no error, while 0.667 indicates a higher one.
The four inputs are tensile strength, hardness, grain size, and elongation.At the same time, rotational speed, transverse feed, and tool tilt angle are the three outputs.The parameters for ANN modeling in the Matlab/Simulink environment are listed in Table 5.

GRG analysis
The coefficient of grey relation for every experiment of the Orthogonal Array is determined with the help of Equation 11.The same is presented in Table 6.

The grade of grey's relational value
The grade for grey relational is calculated by taking an average of all the coefficient of grey relational values, which correspond to each performance characteristic.
where γ i ¼ the grade for grey relational values for the i th experiment and n =the number of performance characteristics.
The higher grade value for grey relational means the experimental value is closer to the ideal normalized value.Table 4 presents the calculated grey relational grade and its order in the optimization process.As shown in Table 6, experiment number 19 has the highest grade for grey relational value.Hence, experiment number 19 is the best multiple performance characteristic among 27 experiments.This is an orthogonal experimental design.The effect of each parameter on the grey relational grade at different levels is shown in Table 7.

ANOVA analysis
To determine the significant parameter that affects the machining parameters of FSP, an analysis of variance (ANOVA) is carried out.Step-1: Sum of the squared deviations Initially, the total sum of squared deviations (SST) from the total mean of grade for grey relational (GR) γ m is obtained as follows: where p = number of experiments in the OA and γ j = mean of the grade for GR for the j th experiment.
The SST is taken from: • a sum of the squared deviations (SSd) due to each process parameter and • a sum of the squared error (SSe).
The following equation gives the contribution of every design parameter in percentage.
From equations 18-19, GR values are calculated.Table 8 shows ANOVA for grade for GR value.

Discussion
After conducting FSP, a tensile test specimen is cut from the process plate.A tensile test was carried out on a universal testing machine (UTM) with a strain rate of 5 ×10 −3 s −1 .After conducting the tensile test, the microstructure of the failed part is checked to observe the fractography of FSP. Figure 5 shows the microstructure of the processed specimen.It is observed that tensile strength improves as grain size goes on reducing.Refer to Table 6 for tensile strength varying according to grain size.

GRG analysis
As shown in Table 7, for the rotational speed of tool parameter, level 2 has a maximum grade for grey relational value; for feed parameter, level 2 has a maximum grade for grey relational value; and for tilt angle parameter, level 2 has maximum grey relational grade.The rotational speed of tool parameter has the first rank, feed the second rank, and tilt angle have the third rank.This shows that rotational speed of tool has the most influence on the output parameters.
A confirmation test is conducted to verify the performance characteristics of FSP.The optimum parameters are selected according to Table 7.Using the optimal level of process parameters, eq. ( 21) is used to estimate GR grade γ- Where, γ m = total mean of the grade for GR value, γ i = mean of the grade for GR value at the optimal level, and q = number of the process parameters significantly affecting multiple-performance characteristics.

ANOVA
The contribution for each term affecting grade for grey relational value is presented in Figure 10.From Table 8, in ANOVA analysis, it is observed that input parameter tool rotational speed is having highest percentage contribution of 79.5% in the FSP; this effect is mainly due to the amount of heat increased due to tool rotational speed and decreased in tool travel feed, which affects grain size (Husain & Mishra, 2021).The feed having a 20% contribution.Whereas tilt angle has just a 1% contribution shown in Figure 11.The increase in TRS and decrease in WS lead to increased heat input to the welded joints.
From ANOVA, it is observed that variable tool angle is having least assistance, about 1%, hence eliminating variable tool angle and using variables rotational speed of tool and travel feed of tool   to predict the performance of ANN.The ANN model in section 3.2 is again implanted for prediction.s It is observed that the ANN with two inputs, rotational speed of tool and feed, has the same performance as the ANN modeled using three inputs, i.e. rotational speed of tool, feed, and tilt angle.The modified ANN has R values of 0.993, 0.991, and 0.967 for training, validation, and testing data sets, respectively, whereas the overall R-value is 0.988 shown in Figures 12 and 13.Thus, modified ANN predicts the process parameters with reasonable accuracy.Hence, modified ANN can be used for modeling and prediction purposes.

Conclusion
In this paper, the optimum process parameters of the FSP of aluminum are studied with the help of an ANN analysis of grey relational and ANOVA analysis.The output process parameters are ultimate tensile strength, percentage elongation, grain size, and hardness.A total of 27 experimental trials is conducted with the input parameter of rotational speed of tool, feed, and tilt angle.
The following conclusions can be drawn: • The mechanical properties, viz.ultimate tensile strength, percentage elongation, grain size, and hardness of aluminum material are determined.
• It is observed that ultimate tensile strength increases with a decrease in grain size.
• ANN model successfully predicts FSP process parameters with an overall R-value of 0.997.
• The value of grade for GR optimal process parameters for FPS are rotational speed of tool, transverse feed, and the tilt angle of 1180 mm/min., 38 mm/min., and 1°, respectively; improved ultimate tensile strength, percentage elongation, grain size, and less hardness are simultaneously obtained.
• The ANOVA of grade for grey relational values shows that rotational speed of tool is the most significant parameter of FSP.
• From ANOVA, it is observed that the variable tilt angle has the least contribution.Hence, an ANN is further implemented using the remaining two variables.The modified ANN predicts with reasonable accuracy.
• This study involves ANN modeling for prediction, GRA gives optimum parameters, and ANOVA yields the most significant parameters of FSP.Thus, this paper implements advanced intelligent techniques to predict, optimize, and determine significant parameters of FSP.This study, the L 27 array is used to experiment and collect data.A higher-order orthogonal array such as L 81 or higher may be implemented.You are free to: Share -copy and redistribute the material in any medium or format.Adapt -remix, transform, and build upon the material for any purpose, even commercially.The licensor cannot revoke these freedoms as long as you follow the license terms.
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Reddy et al. (2020) have proposed GRA to optimize parameters for the laser drilling process.Marichamy et al. (2016) andDey et al. (2017) have proposed GRA to optimize parameters for the electric discharge machining process.Girish et al. (2016) have proposed GRA to optimize parameters for the wear test.For normalizing, each data set value is divided by the average value of that data set.Let, Sequence of original reference numbers = yo(k), Sequence for comparison of original reference numbers = yi(k), where, i = 1, 2, . ..,m; k = 1,2, . .., n, where, m = set of number of experiments, and n = set of a number of observation data.

Figure
Figure 4. FSP test specimen-a) Single-pass FSP and b) Tensile test specimen as per the ASTM-E8 standard.

Figure 5 .
Figure 5. Microstructure specimen after processing.a) Macrostructure of the cut portion.b) Microstructure of NZ.

Figure
Figure 6.a) SEM micrographs and b) EDS analysis of samples obtained for the optimum parameter (1180 rpm.38 mm/ min.and tool tilt angle 1°).
In ANN analysis, MSE variation by epoch for training, validation, and testing is shown in Figure 8.After training, MSE 19.895 is achieved at 9 epochs, and the best validation performance is 3823.455 at 5 epochs.Because the validation error is lowest at the fifth epoch, training was halted then, and weights and biases were used for future modeling.The correlation coefficients between targets (simulation values) and output (i.e., ANN output values) are given in Figure 9 for training, validation, and testing.The training, validation, and testing values are about 0.999, 0.995, and 0.992, respectively.Thus ANN predicts the FSP process parameters with reasonable accuracy.

Figure 11 .
Figure 11.Percentage contributions of factors to the GR grade.

Figure 12 .
Figure 12.ANN performance for input speed and feed.

Figure 13 .
Figure 13.Correlation coefficient for input speed and feed.
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Table 1 . The layout of the L 27 (313) orthogonal array
ANNs use available data, variables, and the training domain to create a trustworthy and robust forecasting network.ANNs are a feed-forward network in which information propagates only one way, ensuring a steady-state network.Refer to Figure2.To design a network, train a network, simulate and validate the network, ANNs required data sets, i.e., input-output data.Data are