Optimization of Grinding Parameters of Tool Steel by the Soft Computing Technique

Grinding is one of the most complex and accurate machining processes, and the efficiency of the grinding wheel depends significantly on its surface properties. This work aims to propose an algorithmic manner that reduces the cost and time to conduct grinding of an optimized DIN 1.2080 tool steel (SPK) using a soft computing technique to obtain the best combination of input parameters including depth of cut (20, 40, 60 μm), wheel speed (15, 20, 25 m/s), feed rate (100, 300, 500 mm/s), and incidence angle (0, 30, 45 de grees) with respect to output parameters consisting of average surface roughness and specific grinding energy. According to the input parameters and their levels, an experiment using fractional factorial design of experiment (RFDOE) was designed. Later on, two parallel feed-forward backpropagation (FFBPNN) networks with similar topology made up of 4, 11, and 1 units in their input, hidden, and output layers are trained, respectively. After sensitivity analyses of networks for determination of the relative importance of input variables, a genetic algorithm (GA) adopting linear programming (LP) based on Euclidean distance is coupled to networks to seek out the best combinations of input parameters that result in minimum average surface roughness and minimum specific grinding energy. The findings revealed that RFDOE provides valid data for training FFBP networks with a total goodness value of more than 1.99 in both cases. The sensitivity analyses showed that feed rate (38.97%) and incidence angle (33.94%) contribute the most in the case of average surface roughness and specific grinding energy networks, respectively. Despite the similar surface quality based on scanning electron microscopy (SEM), the optimization resulted in an optimized condition of the depth of cut of 25.23 μm, wheel speed of 15.02 mm/s, feed rate of 369.45 mm/s, and incidence angle of 44.98 de grees, which had a lower cost value (0.0146) than the optimum one (0.0953). Thus, this study highlights that RFDOE with a hybrid optimization using FFBP networks-GA/LP can effectively minimize both average surface roughness and specific grinding energy of SPK.


Introduction
Te most frequent machining process used to produce a fne surface fnish is grinding. For the purpose of removing material, grinding machines use abrasive wheels. Several factors that impact surface fnish can be generally categorized into wheel and machining factors. Abrasive grains, grit size, bonding material, wheel construction, and wheel grade are among the characteristics of the wheel. Machining parameters include the feed rate, depth of cut, wheel speed, and dressing depth for the grinding wheel [1]. Due to chip deformation resulting in elastoplastic deformation at the primary shear zone, plastic deformation and friction at the secondary shear zone, and elastic deformation and friction at the tertiary shear zone beneath the grinding wheel's cutting surface, there are several areas where material can be removed, thanks to the grinding wheel's structure, which has numerous undefned cutting edges producing a high rate of heat [2][3][4]. In grinding operation, the workpiece material becomes more ductile throughout the process due to the generated heat, which increases chip adherence to the abrasive tool. Heated chips from the grinding zone could have the propensity to lodge the pores of the wheel if they are not entirely eliminated from the cutting zone [5]. Te clogged chips reduce the wheel's ability to cut, increasing the force and temperature of the grinding process and leading to wheel chatter or workpiece thermal damage and wheel loading. Wheel loading, which is related to the dulled wheels, decreases wheel cutting power, and the ensuing excessive rubbing and plowing, which is the propensity of detached chips to stick into the pores of grinding wheels. As a result, it enhances cutting forces and temperature while reducing wheel lifespan. In other words, the cutting forces are increased in addition to the heat fow [6][7][8][9]. Tis kind of damage can be reduced by utilizing food coolant in the grinding zone. Because of the cooling action of the food coolant, the grinding fuids eliminate part of the heat from the workpiece-wheel contact [10]. Some recent works examined adding another auxiliary nozzle in the grinding zone in order to improve efciency. With this regard, using four compressed air nozzle jets at various angles, comprising 0, 30, 60, and 90 de grees, was conducted by Lopes et al. Tey found that employing food coolant, followed by minimum quantity lubrication (MQL) with a compressed air jet at a 30 de grees angle to the wheel surface, is the most efcient method for cleaning the grinding wheel, lowering diametrical wheel wear, and surface roughness [11]. In the following, Hatami Farzaneh et al. used an auxiliary compressed air jet system to investigate the efect of the incidence angle at various angles to clean the wheel surface and reduce wheel loading. Te results showed that an incidence angle of 45 de grees produced the best results in terms of surface roughness, diametrical grinding wheel wear, G-ratio, tangential forces, specif;c energy, and wheel loading analysis [7].
In order to engineer the grinding process of diferent materials through manipulating efective parameters, methods relying on experimental data including support vector machines (SVMs), feed-forward backpropagation neural networks (FFBPNNs), fuzzy logic (FL), and neurofuzzy networks (NFNs) were employed for establishing a relationship to map from input variables to output variables [12,13]. Moreover, researchers utilized diferent methods of optimization such as the golden section search (GSS) method, sequential quadratic programming (SQP) method, genetic algorithms (GAs), particle swarm optimization (PSO), ant colony optimization (ACO), and gray wolf optimizer (GWO), composite desirability function (CDF), and self-learning batch-to-batch optimization (SLBBO) method to seek out the best combination of input variables to reach a desirable value of output parameters [14][15][16].
In the following, we will review works related to the abovementioned topics. With regard to regression-based modeling, Savas and Ozay minimized the surface roughness in the process of tangential turn-milling of SAE 1050 steel by a regression-based model coupled with a genetic algorithm [17]. Bouacha et al. carried out a tentative study on the efect of cutting speed, feed rate, and depth of cut on surface roughness and cutting forces of hard turning with the cubic boron nitrides (CBN) tool of AISI 52100 bearing steel. Trough designing an experiment based on the full factorial design of the experiment (FFDOE), the response parameters were modeled by response surface methodology (RSM).
Ten, a comparison between the optimization performance of RSM and CDF was conducted. Te analogy depicted that RSM eventuates optimized conditions [18]. Elbah et al. designed an experiment based on the FFDOE to assay the efect of depth of cut, feed rate, and cutting speed on the surface roughness of the AISI 4140 steel using two inserts including CC6050WH and CC6050. Furthermore, modeling and optimization by RSM were conducted, and an optimized condition was found [19]. In another work, Bouacha et al. investigated the efect of process parameters consisting of cutting speed, feed rate, depth of cut, and cutting time on response parameters such as tool wear, surface roughness, cutting forces, and metal volume removed of hard turning of AISI 52100 bearing steel with the CBN tool. During their study, Taguchi design of the experiment (TDOE) was carried out. After modeling diferent responses using RSM, the optimization performance of two approaches including CDF and GA was compared. Teir funding highlighted that GA is capable of resulting in better-optimized conditions than DF [20]. Qasim et al. simulated various conditions of machining AISI 1045 steel using ABAQUS software based on the TDOE. Tey considered cutting speed, feed rate, depth of cut, and rake angle in the orthogonal cutting process as afecting variables on cutting forces and temperature. Te optimism condition was determined with regard to statistical calculations [21]. Venkatesan et al. designed an experiment using a central composite design of experiment (CCDOE) with respect to independent variables including cutting speed, feed rate, laser power, and approach angle of the laser beam axis to the tool. During their study, surface temperature and heat-afected depth of Inconel 718 alloy were modeled by RSM. According to the results, coefcients of determination of 0.96 and 0.94 were achieved for surface temperature and heat-afected depth, respectively [22]. Paturi et al. employed TDOE to investigate the efect of parameters consisting of cutting speed, feed rate, and depth of cut on surface roughness and the S/N ratio of turning of Inconel 718. During their study, multiple linear regression models were developed, and optimal statistical condition was determined [23]. Khan et al. adopted a CCDOE to perform multiobjective optimization of surface grinding of AISI D2 steel by the Gray-Taguchi method using depth of cut, table speed, cutting speed, and minimum quantity lubrication fow rate as input variables. Te output variables were surface quality, surface temperature, and normal force. Te objective functions were based on RSM. Tere were desirable results through the proposed optimization procedure [24].
Turing to ANN-based modeling, Davim et al. trained an FFBPNN with two outputs including average roughness and maximum peak-to-valley height of steel 9SMnPb28k (DIN) feeding feed rate, cutting speed, and depth of cut as efecting process parameters. To obtain data, the FFDOE was selected. A high value of the coefcient of determination (COD) was acquired in both responses [25]. Muthukrishnan and Davim applied the FFDOE considering cutting speed, feed rate, and depth of cut as efecting factors on the surface roughness of Al-SiC (20 p). Ten, a model based on the FFBPNN was constructed. During the verifcation of the model, the 2 Computational Intelligence and Neuroscience maximum percentage of prediction error was 4.78% [26]. Çaydaş and Ekici compared the predictability of three different types of SVMs tools such as least square SVM (LS-SVM), spider SVM, and SVM-KM and an FFBPNN through a study to predict the surface roughness of AISI 304 austenitic stainless steel under CNC operation. Te input parameters of the models were cutting speed, feed rate, and depth of cut. In order to acquire the data, a three-level FFDOE was employed. Unlike most studies, all SVMs models had better performance than FFBPNN [27]. Farahnakian et al. presented an algorithmic method based on FFBPNN as a predictive model and PSO as an optimizer for the personalization of polyamide-6/nanoclay (PA6/NC) nanocomposites products using the milling process. Under changing parameters such as spindle speed, feed rate, and nanoclay (NC) content, the cutting forces and surface roughness were minimized [28]. Davim tried to optimize surface roughness, tool wear, and power required through the manipulation of parameters such as cutting speed, feed rate, and cutting time taken from another study [29].  [40]. Almost all researchers focused only on the optimization of surface roughness while less consideration has been made about specifc grinding energy which is a factor that makes a remarkable contribution to the grinding process. Herein, to optimize the grinding parameters such as depth of cut, wheel speed, feed rate, and incidence angle to obtain tool steel with minimum surface roughness and minimum specifc grinding energy, an experiment based on the fractional factorial design of experiment (RFDOE) is designed. Ten, two parallel models via an FFBPNN consisting of four, eleven, and one node in input, hidden, and output layers are developed, respectively. Furthermore, the relative importance of input variables is analyzed. Later on, a cost function is determined and optimized by a GA to fnd the best individual. Finally, the optimized sample was produced and compared with the optimum sample to verify the applicability of the proposed optimization algorithm.
Computational Intelligence and Neuroscience 3

Workpiece Material.
Te material employed in the reciprocal grinding tests was DIN 1.2080 tool steel (SPK), high carbon, high chromium tool steel that has outstanding resistance to wear and abrasion and is often used in a range of mechanical applications including high-performance blanking, punching dies, and plastic molds. Te SPK sample purchased from (https://www.tejarataliaj.com/) with dimensions of 20 × 30 × 10 mm 3 had a hardness of 250 HB. In order to reduce the residual stress and hardness that might have been produced during the casting and cutting process, before the grinding process, all the samples underwent a heat treatment process as given in Table 1.
Te chemical composition of this material is displayed in Table 2.

Experimental Design.
To investigate the efect of independent variables with three diferent levels including depth of cut, wheel speed, feed rate, and incidence angle (nozzle angle) on average surface roughness (R a ) and specifc grinding energy (E e ), an experiment based on Table 3 using the RFDOE is designed.
Te total number of samples has been determined according to the RFDOE model [16,41] as equation (1) utilizing Design-Expert 13 software: where μ, D i , V j , R k , A l , and ε (ijkl)m are the common efects for the whole experiment, ith level of depth of cut, jth level of wheel speed, kth level of feed rate, lth level of incidence angle, and random error of mth repetition, respectively. Te two combinations of variables indicate the interaction between them. Moreover, the average surface roughness and specifc grinding energy [42][43][44][45][46] are calculable using equations (2) and (3), respectively: where L refers to the sampling length. In addition, F t , V, W, R, and D are the tangential grinding force, the cutting speed, the contact width (20 mm), the feed rate, and the depth of cut, respectively.

Methodologies.
In this study, according to ISO 468:1982, BLOHOM Surface Grinder was employed for grinding (model HFS204). Te grinding machine was outftted with NORTON White Alumina-32A46 JVBE 268445 vitrifed bond grinding wheel. During grinding, the tangential force was extracted using the dynamometer, which is manufactured by the KISTLER Company in Germany (model 92558). Input parameters are summarized in Table 4.
Marsurf XR 1 surface roughness tester was employed to measure R a values. According to equation (2), R a is the arithmetic average of the absolute profle height values across the sampling length, which was set at 0.80 mm. Moreover, the standard wheel dimension was 225 × 37 × 51 mm 3 . Te distance between the nozzle and the wheel surface was chosen to be 1 mm. Conventional cutting fuid (semisynthetic oil-based emulsion) was used as the food coolant. Te grinding wheel was dressed using a diamond single-point tool with a depth of 50 μm in two passes under the speed of 100 mm/ min to obtain a wheel surface free of chips and particles after each experimental test, and its spark-out was set at 8 seconds. Additionally, the pressure of the compressed air nozzle and its dimensions was 0.70 MPa and 10 × 1 × 100 mm 3 , respectively. Figure 1 indicates the arrangement of the experimental setup and its schematic view.
Te dynamometer has been set up on the bed, and a fxture has been placed above it to hold the samples. Te grinding zone contains two embedded nozzles, one for the delivery of coolant and the other for the jet of compressed air. A diamond single-point dressing mechanism has been placed on the other side of the fxture so that the time spent getting dressed can be reduced to a minimum.

Modeling and Optimization
3.1. Artifcial Neural Network. In terms of predictions, artifcial neural network-based models are considered as the most efcient ones. Among many networks, the FFBPNN is utilized to predict the output of the diferent systems with desirable performance. Besides, the most critical aspect during modeling with ANN is the number and validity of data obtained by performing an experiment with a particular design. Diferent designs including FFDOE, CCDOE, and TDOE can be taken into account to provide data for training and testing networks. In the present study, the data are obtained via the fractional factorial design of experiment     Computational Intelligence and Neuroscience (RFDOE) which considers the main and two interactions. In order to evaluate the performance of networks during training and testing steps, the same total goodness function (TGF) is considered [16,[47][48][49]. Besides, to enhance the performance of networks, two parallel networks with single output instead of a network with dual outputs are developed. Te following functions are used for the performance evaluation of networks.
Te basic components of a neural network are neurons, inputs, weights, a summation function, an activation function, and an output [35,50]. Here, in this work, t i , O i , t, and n are the target, output, mean values of the target, and amount of data during the testing or training step of the network, respectively. In addition, M is the total amount of data. Table 5 depicts the performance of the networks using diferent activation functions.
Referring to the total goodness value of diferent activation functions, the activation function of hidden and output layers has been determined as equations (5) and (6), respectively [51]: Purelin(n) � n.
Te learning rate and momentum value were both 0.90. All available training functions such as Levenberg-Marquardt, BFGS quasi-Newton, resilient backpropagation, scaled conjugate gradient, conjugate gradient with Powell/Beale restarts, Fletcher-Powell conjugate gradient, Polak-Ribiére conjugate gradient, one step secant, and variable learning rate backpropagation have been tried, and there was no diference in their TGF values. Tus, to improve the training process as in previous work [52], the Levenberg-Marquardt algorithm has been chosen as a training function. Te number of training cycles was 1000 epochs. Both networks have a single hidden layer. Table 6 depicts the setting of ANN-based models.
In order to specify the number of units in the hidden layer, a comparison between total goodness values was made. Te abovementioned networks are developed via the ANN toolbox of MATLAB software.

Genetic Algorithm.
A genetic algorithm is an adaptive method of optimization that is inspired by biological organisms. Tis procedure is based on the "survival of the fttest" that rules in natural selection, and its basic fundamentals were frst afrmed by Holland [53]. By promoting the survival and reproduction of the solutions that are most likely to converge toward the optimum, these algorithms build a population of solutions and cause them to develop [54,55]. Since it is reliable in identifying an optimal solution, which is the nearly global minimum, GA is one of the most alluring strategies for problem optimization in the numerous domains of industrial application [16,56]. Trough implementing such procedures, solutions are represented as vectors called chromosomes. During the optimization process, such chromosomes are sorted according to their either cost or ftness values which are defned by objective function or functions [14]. Te process of fipping a chromosome is known as mutation. To commence optimization, the setting of the GA algorithmic toolbox of MATLAB software is considered as given in Table 7. Te chromosomes change throughout a number of generations or iterations. By combining crossover and mutation, new generations are produced. In a process known as a crossover, two chromosomes are divided and then combined with each other. Later on, the chromosomal bit is fipped during a mutation. Te best chromosomes are maintained while the inferior ones are eliminated after the chromosomes have been assessed using a set of ftness criteria. One chromosome is chosen as the best option for the problem after this procedure is repeated until it has the best ftness [57]. In fact, the genetic algorithm uses the criteria to determine the objective function's global minimum value and makes sure the output is the converged value. In light of this, genetic algorithms are efective tools for enhancing process parameters to identify the best-ft optimal solution from the global search based on the specifed goal function to reduce average surface roughness [58]. Te size of the original population, the kind of selection function, the crossover rate, and the mutation rate are the main factors that have the greatest infuence on the best outcome and must be taken into account. Trial and error are used to determine the value of parameters for these criteria in order to get the desired outcome as efciently as possible.
Regarding previous works, it can be deduced that most researchers had not considered the specifc grinding energy which is the main parameter to determine the energy required for obtaining a particular average surface roughness. In this study, a multiobjective optimization is constructed based on two responses including average surface roughness and specifc grinding energy. In the optimization step, both trained networks for average surface roughness and specifc grinding energy are recalled, in which their value is normalized between 0.10 and 0.90. Ten, a Euclidean distance [59] as equation (7) to fnd an individual with minimum average surface roughness and minimum specifc grinding energy is applied.
where x → , R n , and E n are the vectors that store input parameters, the normalized average surface roughness, and the normalized specifc grinding energy, respectively. In addition, D, V, R, and A refer to the depth of cut, wheel speed, feed rate, and incidence angle, respectively. Te upper and lower boundaries of input parameters are as follows: Te schematic illustration of the experimentation, modeling, and optimization process is highlighted in Figure 2.
According to Figure 2, the data are normalized after obtaining them from an experiment based on the RFDOE. Next, ANN-based models are trained and tested via dataset. Later on, the GA operator is utilized to fnd an individual that can result in minimum average surface roughness and specifc grinding energy.

Statistical Results.
Te results of the investigation on average surface roughness and specifc grinding energy for 60 samples under alteration of the depth of cut, wheel speed, feed rate, and the incidence angle with a 95% confdence level are summarized in Table 8. All estimations are based on three repetitions.
Using equation (10), the raw data obtained through experimentation are normalized for the modeling step between 0.10 and 0.90 to avoid any quantitative efect [16,60]: where Y and Y n are the actual and normalized values of variables, respectively. Besides, to train and then test models, the dataset randomly was split into a ratio of 54 : 6. Regarding the information provided in Table 8, Figure 3 demonstrates the efect of diferent cutting parameters on average surface roughness and specifc grinding energy. According to Figure 3(a), when the depth of cut was increased from 20 to 40 μm, average surface roughness rose from 0.62 to 0.92 μm, respectively. Meanwhile, the reverse efect can be found in Figure 3(b) regarding specifc grinding    Figure 2: Optimization diagram of the hybrid model.  Figure 3(c) that there is no signifcant alteration in terms of average surface roughness. At the same time, specifc grinding energy underwent a growth to reach a maximum value of 27.07 J/mm 3 at a wheel speed of 25 m/s as shown in Figure 3(d). On the other side, it can be seen in Figure 3(e) that the lowest average surface roughness (0.70 μm) belonged to a feed rate of 100 mm/s while the highest one (0.87 μm) was a feed rate of 300 mm/s. In addition, based on Figure 3(f ), a higher feed rate (100 mm/s) led to higher specifc grinding energy (44.30 J/mm 3 ). Finally, changing the incidence angle from 0 to 45 de grees, as depicted in Figure 3(g), resulted in a reduction of average surface roughness from 1.03 and 0.63 μm, respectively. Te same trend can be found in Figure 3(h) with regard to specifc grinding energy. In other words, the higher the incidence angle (45 de grees), the lower the specifc grinding energy (17.87 J/mm 3 ) was required. Physically speaking, it can be said that when the depth of cut, feed rate, and wheel speed is increased, the temperature at the interface witnesses an increase that leads to the elevation of average surface roughness [35,61,62]. In addition, the reduction of the incidence angle from 0 to 45 de grees is investigated, and it is shown that when the angle of the nozzle is 45 de grees, a large amount of fuid is carried to interface regions which enhances the lubrication and reduces the grinding zone temperature. As a result, lower average surface roughness is achieved [62].
In terms of specifc grinding energy, it is shown that a higher depth of cut causes lower specifc grinding energy due to plowing and rubbing actions. In fact, the girt sharpness and grinding force are the driving forces behind the reduction of the energy [62,63]. Trough rising wheel speed, the specifc grinding energy goes up due to the growing cutting force. Hence, specifc grinding energy ascents [64,65]. Moreover, a high feed rate provides a condition in which that more volume of material is removed due to higher penetration of grits. Terefore, specifc grinding energy falls [66]. Similar to roughness, when the nozzle angle is 45, an optimum value of specifc grinding energy is obtained due to better cleaning and cooling and lower grinding zone temperature [7,62].

Developed Objective Functions.
A hidden layer, an output layer, and an input layer are frequently used to model artifcial neural networks. Te input layer regulates the  process variables for feed rate, wheel speed, and depth of cut. Te hidden layer was populated with the number of neurons required to increase the output value's accuracy. When employing a multilayer feed-forward network to solve realworld issues, one of the most crucial factors to take into account is the size of the hidden layers [67,68]. Te best network is chosen based on the total goodness value. Te architecture of developed ANN-based models for average surface roughness and specifc grinding energy is shown in Figure 4. Such architecture is an optimum one that can result  in the highest total goodness value in both cases. Besides, it is worth mentioning that 300 runs for each topology have been taken into account due to their stochastic nature and the weight and bias values of the best-performing one are reported. Figure 5 indicates the performance of ANN-based models including average surface roughness and specifc grinding energy during training and testing steps.
It can be found from Figure 5 that the capability of developed networks during both training and testing is desirable with the remarkable determination of coefcient ( ∼ 1). Te training process of average surface roughness and specifc grinding energy fnished after 128 and 296 epochs, respectively. However, there are a few negligible settlement regions during the testing steps. Overall, ANN-based models had an excellent capability to result in a high value of TGV. Table 9 quantitatively outlines the performance of the ANNbased models.
According to Table 9, it can be said that both trained networks have more than a 1.99 total goodness value, which demonstrates their high predictability. To construct such models as two objective functions, their bias and weight values are extracted and summarized in Tables 10 and 11.
Te next phase of modeling is to analyze the sensitivity of the developed ANN-based models. Such analysis determines the impact of each input unit on the output of the network. Equation (11) will be utilized to assess the sensitivity analysis of diferent input variables ( I i ) on the output of the network [69]: According to equation (11), when the value of a specifc input variable is high, it will make more contributions to the output of the network. Te results of the calculation are depicted in Figure 6.
With regard to Figure 6, it can be realized that the most percentage of average surface roughness and specifc grinding energy belong to incidence angle (38.97%) and feed rate (33.94%), respectively, while cutting speed (10.08%-17.98%) has the least percentage in both cases. Turing to feed rate in the case of average surface roughness (17.26%), its percentage is almost half the specifc grinding energy one. On the contrary, the incidence angle in the case of specifc grinding energy (21.83%) is approximately half the percentage of average surface roughness one. Moreover, the depth of cute contributes 33.69% and 26.25% with respect to average surface roughness and specifc grinding energy, respectively.

Results of Optimization.
When optimization is commenced, GA starts ranking individuals according to their cost value to reach out to an individual with the minimum possible cost value regarding input variables. In this study, the cost value of an individual is determined in a way that the individual with the lowest Euclidean distance to minimum average surface roughness and minimum specifc grinding energy will be chosen as the best one. Figure 7 indicates the performance of GA during optimization.
It is worth pointing out that Figure 7 is the best-performing result of 10 runs due to the stochastic nature of GA. As it can be found, the best cost value reduces during the advancement of GA until it reaches 0.0176 value over 25 generations with an initial population size of 25. Moreover, the diversity of individuals is good enough to avoid reaching local minima as a result of applying a mutation fraction of 0.50. Table 12 compares the cost value of the optimum samples and optimized the ones considering the value of corresponding input variables and GA parameters.
With regard to Table 12, it can be realized that when the population size increases, the cost value decreases. In addition, the higher the mutation faction value, the lower the cost value will be achieved. Tus, the simulated sample 10 with the highest population size and the most mutation fraction has the lowest cost value than the optimum one and other simulated ones. Regarding Table 12, the average surface roughness and specifc grinding energy were reduced by 1.0308 and 2.7662 times in comparison with the optimum sample, respectively. Tus, the cost value declined from 0.0953 to 0.0146. Such reduction is the result of increasing the depth of cut from 20 to 25.23 μm, keeping wheel speed and incidence angle almost constant and rising the feed rate from 300 to 369.45 mm/s. Based on the results, both depth of cut and feed rate has a direct efect on average surface roughness while an indirect efect can be found in the case of specifc grinding energy. Te point is that the constructed cost function (equation (7)) acts as a trade-of function between average surface roughness and specifc grinding energy to fnd an optimized condition. To verify the result of Depth of cut 1-1    optimization, simulated sample 10 was fabricated according to input variables. Figure 8 depicts the workpiece, SEM image, and average surface roughness profle of optimum and optimized samples (simulated sample 10 in Table 12).   roughness profle of the optimized one showed the lowest peaks and valleys. In fact, optimization not only improved the surface properties quantitatively but also resulted in a similar qualitative state of the surface.

Conclusion
In the following work, an experiment with a total sample of 60 using a fractional factorial design of experiment based on four independent parameters of the grinding process with three levels including the depth of cut (20, 40, 60 μm), wheel speed (15, 20, 25 m/s), feed rate (100, 300, 500 mm/s), and incidence angle (0, 30, 45 de grees), and two dependent parameters of surface quality consisting of the average surface roughness and specifc grinding energy was considered. Ten, data were split into 90 : 10 for training and testing two parallel feed-forward backpropagation neural networks with similar inputs but diferent outputs. Next, the output of networks was fed to a genetic algorithm to seek out an individual with a minimum value of average surface roughness and a minimum value of specifc grinding energy utilizing a Euclidean cost function. Finally, the optimized sample was fabricated to verify the optimization result. Te conclusions are as follows: (1) Te fractional factorial design of experiment is capable of providing valid data similar to response surface methodology for a feed-forward backpropagation neural network to reach around a total goodness value of 2 (2) Te proposed algorithmic procedure is not only able to fnd better individuals (average surface roughness value of 0.39 μm and specifc grinding energy value of 4.79 J/mm 3 ) than already one (average surface roughness value of 0.40 μm and specifc grinding energy value of 13.25 J/mm 3 ), but it is efcient to reduce the required time and cost value for engineering the grinding process.