Introduction
A manufacturing process is an act of converting the raw material into a finished product (Mörtl and Schmied, Reference Mörtl and Schmied2015). During manufacturing a product, several variations are encountered like machine vibrations, operator skill level, and wear out in machine and cutting tool. Therefore, it is impossible to manufacture the products with theoretically exact dimensions as specified in the drawing. Considering the manufacturing difficulties, the design engineers specify tolerances to a basic dimension. Tolerance is defined as the maximum permissible deviation from the basic dimension (ASME, 2009). Manufacturing tolerance is a plus or minus deviation from the basic dimension on a product size. If the machined part lies within the tolerance span, the product is accepted else rejected/reworked. In addition to it, the specified manufacturing tolerance value must ensure product functionality (Srinivasan et al., Reference Srinivasan, Wood and McAdams1996; Saravanan et al., Reference Saravanan, Jerald and Delphin Carolina Rani2020), interchangeability (Pierre et al., Reference Pierre, Teissandier and Nadeau2009), and customer requirements (Chandrasegaran et al., Reference Chandrasegaran, Ramani, Sriram, Horváth, Bernard, Harik and Gao2013). Generally, design engineers prefer closer tolerances for better product functionality; on the contrary, manufacturing engineers expect liberal tolerances (Yang et al., Reference Yang, Marefat and Ciarallo1997). The manufacturing cost–tolerance relationship is presented in Figure 1.
Manufacturing cost–tolerance relationship.
Practically, closer tolerances ensure superior functionality; however, it leads to increased manufacturing cost. On the other side, liberal tolerances increase productivity, but product quality and functionality are a concern. In addition to it, design engineers need to concentrate on other various factors ahead of tolerance design like functionality, quality, safety, delivery time, producability, and cost (Hayes and Sun, Reference Hayes and Sun1995). Traditionally, experienced design engineers were engaged to design tolerance values (Geraci et al., Reference Geraci, De Tullio and Iaccarino2017). However, they specified tolerance values with several iterations and were not consistent and realistic.
This paper proposes an explicit neural network-based manufacturing cost–tolerance modeling approach. The paper is organized as follows. The section "Proposed methodology" presents the proposed method of modeling the manufacturing cost–tolerance relation. Two case studies were demonstrated with the proposed method in the section “Case study”, followed by results and discussion in “Major improvements due to the network models”.
Manufacturing cost–tolerance modeling overview
Manufacturing cost is the machining cost incurred to manufacture a product. Generally, the dimensions are specified with the tolerance values, in which closer tolerances will increase the manufacturing cost, and liberal tolerance will decrease the manufacturing cost (Diplaris and Sfantsikopoulos, Reference Diplaris and Sfantsikopoulos2000). Practically, this relation is always nonlinear (Homann and Thornton, Reference Homann and Thornton1998), and it is difficult for researchers to depict the same behavior theoretically (Geraci et al., Reference Geraci, De Tullio and Iaccarino2017). Manufacturing cost–tolerance modeling is a method to capture the complex interaction between the tolerance values and manufacturing cost. In order to develop cost-efficient products, the specified tolerance must be practically realistic (Mörtl and Schmied, Reference Mörtl and Schmied2015). In the past, the nonlinear manufacturing cost–tolerance relation was approximated as a linear function for easy calculation and optimization (Ngoi, Reference Ngoi1992). With this approximation, the exact knowledge behind the manufacturing cost–tolerance relation is completely lost. Initially, the manufacturing cost–tolerance relation was developed as an extension of Taguchi's loss function (Prabhaharan et al., Reference Prabhaharan, Asokan, Ramesh and Rajendran2004). Gradually, probability-based models were also developed considering the manufacturing process with a normal distribution (Liu et al., Reference Liu, Jin, Wang and Xie2014). In the analysis of a manufacturing cost–tolerance model, the manufacturing process involves various machining characteristics. A number of mathematical models were developed using linear and exponential functions (Saravanan et al., Reference Saravanan, Balamurugan, Sivakumar and Ramabalan2014), combined square and exponential functions (Lee and Kwon, Reference Lee and Kwon2013). When the capability of the model increases, the error function governing the model was also found increasing (Reed and Gillies, Reference Reed and Gillies2016). To accurately model the relations, higher-order polynomial equations were used (Su and Wakelam, Reference Su and Wakelam1999). Apparently, the cubic polynomial model was introduced (Islam, Reference Islam2009) and found to be good with a comparatively lesser error. Fourth- (Janakiraman and Saravanan, Reference Janakiraman and Saravanan2010) and fifth-order (Balamurugan et al., Reference Balamurugan, Saravanan, Dinesh Babu, Jagan and Ranga Narasimman2017) polynomial equations were developed based on the cubic model. In order to precisely map the parameters, a spline model (Homann and Thornton, Reference Homann and Thornton1998) was developed, which was more complex than the regular curve fit models. But, they were not suitable for multi-input (variable) problems; just they were good for single input (variable) problems. Table 1 presents the various manufacturing cost–tolerance models.
Various manufacturing cost–tolerance models
a, b, c, and m are the coefficients of the function, t is the tolerance value, and CTF is the cost–tolerance function.
In a concurrent manufacturing environment, models lacked to grasp the real situation. Generally, products undergo various stages of machining operations in many machines (Alex et al., Reference Alex, Chavez and Davy2019). Hence, various activities are indulged in the process. An activity-based model, including the operational variations (Hu et al., Reference Hu, Xiong and Wu2004), was developed. A concurrent model (Huang et al., Reference Huang, Zhong and Xu2005) was extensively developed to map the relation with multiple activities taking place in the process. In order to address the mechanical parts, a new model (Sanz-lobera et al., Reference Sanz-lobera, Sebastián and Pérez2010) was designed with hybrid functions. Graphical methods were developed as an alternative to the existing models. Tolerance charts (Ngoi et al., Reference Ngoi, Agarwal and Chua1998; Shen et al., Reference Shen, Shah and Davidson2008) were developed. For each product, a special chart with a product drawing was developed. Individual dimensions were designated from the origin, and the designer assigns the tolerance value. This graphical method was further extended to assemblies (Ashiagbor et al., Reference Ashiagbor, Liu and Nnaji1998). With the increase in the number of parts, the chart gets complex, and interpretation was difficult. Moreover, the graphical solutions produced were of conservative estimations and far behind the realistic situations (Tsai and Cutkosky, Reference Tsai and Cutkosky1997).
Synthesis
The nonlinear manufacturing cost–tolerance relationship was essential and crucial for engineers during the design and process planning stage. These models are used to design and optimize the tolerance values, estimate the manufacturing cost, and determine the processing sequence. From the literature, it was evident that mathematical models were developed through curve fitting. The following challenges persist in the existing methods.
1. Exponential functions, higher-order polynomial equations, power functions, and hybrid functions were the commonly used models. Regardless of the fitting model adopted, the error function is still present, and it cannot be overlooked. This error function depicts the deviation of the experimental value and the theoretical model.
2. The traditional curve fit models are suitable for a single input (variable) and output problems and cannot be used for multi-input (variable) problems.
3. Essentially these models have not focused the part size geometry. The irony of them is two parts with the same tolerance value of different sizes and will have the same manufacturing cost. Since the models do not consider the part size.
4. A common universal mathematical model will not be suitable for all industries with varying manufacturing infrastructure and potentials.
Neural networks overview
A complex nonlinear relationship exists between the manufacturing cost and its tolerance value. If the tolerance value is too rigid, the manufacturing cost increases and vice versa. Neural networks are good tools to interpret the interactive patterns in the data set. This property enables them to model the correlation between the input and output variables of a system. The neural network model consists of input neurons depicting the input variables. The sum of these input signals is multiplied by weight coefficients (Kontovourkis et al., Reference Kontovourkis, Phocas and Lamprou2015). The output signal of the model is the sum of the elements, which is subjected to a nonlinear activation function. The difference in the output and input signals is computed, and the weight coefficients are modified appropriately (Wolbrecht et al., Reference Wolbrecht, D'Ambrosio, Paasch and Kirby2000). The learning algorithm determines the accuracy and convergence time for input and output correlation (Yang et al., Reference Yang, Marefat and Ciarallo1997). To develop the neural network-based cost–tolerance model, three different types of neural networks such as multilayer perceptron (MLP), backpropagation network (BPN), and radial basis function (RBF) with different architectures were used.
Multilayer perceptron
MLP is often viewed as a logistic regression classifier. It is a supervised training neural network, in which the mapping of the input sample to the output is purely governed by the synaptic weights of the input and output layers (Kukolj et al., Reference Kukolj, Berko-pusic and Atlagic2001). It has good nonlinearity in mapping the input and output values. During each training set, the difference between the output function to the input target value is computed (Babić et al., Reference Babić, Nešić and Miljković2011). However, the hidden layers and its activation function determine the premise of deeper learning property.
Backpropagation network
BPN is a forward supervised learning network. The corresponding weights of the input and output neurons were adjusted based on the deviation between the input target and output values. The BPN is superior for single output problem and overdetermines the target values if the output neurons are increased (Carpenter and Hoffman, Reference Carpenter and Hoffman1997). A feedforward BPN is often found best in nonlinear adaptability (Saravanan and Jerald, Reference Saravanan and Jerald2019) and data generalization (Lin and Chang, Reference Lin and Chang2002). For proper learning and convergence, the network parameter's learning rate and momentum coefficient must be precisely identified.
Radial basis function
RBF is considered as a simple layer type of artificial neural network typically used to approximate the given functions. They can model any nonlinear function using their single hidden layer and can be easily trained (Rojek, Reference Rojek2017). The correlation between input and output data set is completely based on the activation function in the hidden and output layers, respectively.
Proposed methodology
In this modernized globally competitive world, design engineers are in need of an easy and realistic method to design tolerances. The basic procedure to perform a manufacturing cost–tolerance model involves production data. For various tolerance values, the experiments were carried out in the machine shop, and the time required to machine a particular part was observed and converted into the equivalent cost. Unlike the traditional models, the proposed neural network models were broadly classified into a prismatic and rotational network. The best neural network model was set as a fitness function, and the genetic algorithm (GA) was used to optimize the model. Figure 2 shows the proposed methodology.
Proposed methodology.
Workpiece geometry-based network model
The proposed method aims to develop realistic neural network models considering the basic geometry and part size. Based on the geometry, any product can be broadly classified into prismatic and rotational geometry. Components with planar machining features are called prismatic geometry, and with cylindrical machining, features are called rotational geometry. The part size of the respective geometry is specified as per the nomenclature is shown in Figure 3. The neural network model for prismatic geometry has the length (L), breadth (B), and thickness (T), whereas for rotational geometry, the diameter (D) and length (L) were considered. These designated nomenclature's serve as an input to the neural network model. In addition to these inputs, tolerance value (TV) is also assigned as an input neuron. The output neuron for the network model represents the manufacturing cost (MC). Thus, two independent neural network models were developed for prismatic and rotational components, respectively.
Prismatic and rotational geometry nomenclature.
Manufacturing cost–tolerance data set
In order to specify realistic tolerance values, it is essential to use a proper manufacturing cost–tolerance relationship data. In practice, the empirical manufacturing cost–tolerance relationship data should be obtained from the workshops through experiments or observations (Mörtl and Schmied, Reference Mörtl and Schmied2015). Table 2 illustrates the data set attributes along with the workpiece sizes used in the experiment for prismatic and rotation geometry, respectively. The experiment was performed in the tolerance span of 0.001–0.05 mm. Based on these workpiece attributes, separate experiments were performed for prismatic and rotational products. The time taken to machine the product was carefully observed and the machine hour rate is expressed as the manufacturing cost (in dollars). Table 2 presents the production data set obtained from the experiments for respective prismatic and rotational geometry, respectively.
Manufacturing cost–tolerance data set
Construction of the neural network model
The following data are fed to the prismatic neural network as input: i 1 = length (mm), i 2 = breadth (mm), i 3 = thickness (mm), and i 4 = tolerance value (mm). Similarly, for the rotational neural network, i 1 = diameter (mm), i 2 = length (mm), and i 3 = tolerance value (mm) are assigned to the input neuron. The corresponding machining cost (dollars) is considered as the network output. The basic network construction for the prismatic and rotational models is presented in Figures 4 and 5, respectively.
Basic prismatic network model.
Basic rotational network model.
Determination of neural network architecture
The architecture of the neural network comprises the input, hidden, and output layers. The neurons in input and output layers represent the variables of the problem statement, whereas the number of hidden layers and the corresponding neuron counts will determine the learning ability of the network model (Rojek, Reference Rojek2017). If the hidden layers and its neurons are small, the network's learning ability will be poor. Subsequently, if they are large, it overburdens the network model and leads to poor correlation (Bukharov and Bogolyubov, Reference Bukharov and Bogolyubov2015). The thumb rule to calculate the hidden neuron was found in the literature as
$$M = n + 0.618 \times \lpar {n-1} \rpar $$where M is the number of hidden neurons, and n is the number of input layer neurons and the basic network model was created as per it (Wang and Huang, Reference Wang and Huang2009). The manufacturing cost–tolerance data set was randomly partitioned into three files for training (75% of the data), testing (15% of the data), and validation (10% of the data). The network model was trained with a training file and tested using the training file. In addition to it, the verification was performed with the validation file. Validation is specially performed to address the overfitting issues.
Network models were continuously trained with two termination criteria. The first criterion was the number of epochs (iterations), and the second was the attainment of predefined root-mean-square-error (RMSE) value of less than 0.05. After each epoch, the RMSE value was calculated for the different neural network models (MLP, BPN, and RBF). The best combination with minimum RMSE was decided as the architecture. The overall evaluation of the neural network model was done assessing the simulated value from the network and by correlating them with the manufacturing cost–tolerance data set. The greater are the accuracy and the degree of certainty; better is the regression coefficient to a maximum of 1.
GA optimization
The optimization process finds the best solution for the problem with constraints. The proposed approach integrates the neural network model with the GA to obtain the optimum value. The procedure to implement the integrated GA is as follows:
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Step 1: Set the population size to 100 and the objective function, minimization of manufacturing cost.
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Step 2: Define the selection method.
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Step 3: Define the crossover method and the rate to produce the offspring population.
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Step 4: The mutation rate was defined to mutate the individuals.
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Step 5: Repeat step 2 until satisfactory results are obtained.
The proposed integrated GA was developed with five selection and crossover methods. The five selection methods are absolute top mate selection, tournament selection, Roulette wheel selection, rank selection, and top mate selection. The five methods of the crossover are uniform crossover, one-point crossover, two-point crossover, intermediate crossover, and line crossover. The better solutions were observed in various combinations rather than adopting a set of parameters predefined in the literature. The strategy of changing the crossover and selection methods combination directly affects the solution, and the best offspring were selected based on the minimum manufacturing cost. Similarly, the crossover and the mutation rate were changed from 0.1 to 0.9, with an increment of 0.1.
Case study
In this section, the application of the proposed method is carried out. Initially, the network models were trained, tested, and validated with the manufacturing cost–tolerance data set. Later, the best network model was defined as the objective function, for which GA was applied to obtain optimum results. The first case study is a gearbox assembly (Kumar et al., Reference Kumar, Padmanaban, Kumar and Balamurugan2016) consisting of rotational parts and second, a two pin-two hole assembly (Saravanan et al., Reference Saravanan, Balamurugan, Sivakumar and Ramabalan2014) with prismatic and rotational parts.
Determination of the neural network architecture
The basic network models presented in the section “Construction of Neural network model” were trained with the manufacturing cost–tolerance data set. Initially, the architecture was set with the hidden neurons as per Eq. (1), and it was changed based on the learning ability and its performance. From the analysis as presented in Table 3, for the prismatic network model, BPN 4 × 4 × 5 × 5 × 1 network model (Fig. 6) with four input neurons, four neurons in the hidden layer 1, five neurons in hidden layers 2 and 3, respectively, and one output neuron has performed well. When compared to the other network models, R 2 was found best with 0.9897 and RMSE was 0.0094. Similarly, for the rotational network model, 3 × 3 × 3 × 1 BPN network model (Fig. 7) with three inputs, three neurons in hidden layers 1 and 2, respectively, and one output neuron has good performances over the other models. Tables 3 and 4 present the network model's performance for prismatic and rotational geometry, respectively. The relation between the manufacturing cost–tolerance obtained from the best BPN model for the prismatic and rotational geometry is shown in Figures 8 and 9, respectively. The best BPN models for respective prismatic and rotational geometry were defined as the objective function to minimize the manufacturing cost.
Best prismatic 4 × 4 × 5 × 5 × 1 BPN network model.
Best rotational BPN 3 × 3 × 3 × 1 model.
Manufacturing cost–tolerance curve for prismatic geometry.
Manufacturing cost–tolerance curve for rotational geometry.
Network model parameters for prismatic geometry
Network model parameters for rotational geometry
Gearbox assembly
The gearbox assembly shown in Figure 10 requires tolerance value specification for the dimensions A, B, C, D, and E. Dimension A is the bore depth of the case component, and dimension B is the bore depth in the housing unit. The length of the shaft is designated as dimension C. Dimensions D and E are the collar thickness for bush 1 and 2, respectively.
Step 1 : The input data file consisting of the geometry and size of the part dimensions are tabulated as shown in Table 5. This input file was fed to the best rotational network model and the output was simulated.
Step 2 : The trained and simulated rotational network model was assigned with an objective to minimize the manufacturing cost. The GA was run with a population size of 100. By the trial and error method, the genetic parameters were tuned.
Step 3 : This step focuses on obtaining the best optimal tradeoffs from the GA. By the trial and error method, the genetic operators were continuously changed and the best results were obtained with the following combinations: the uniform crossover method at a 0.8 crossover rate and the Roulette wheel selection method.
Step 4 : The optimum tolerance values for the dimension from the genetic optimization algorithm along with its optimal manufacturing cost is detailed in Table 6.
Gearbox assembly.
Input data for the gearbox assembly
Gearbox assembly result and comparison
Two-pin-two-hole assembly
The two-pin-two-hole assembly consists of two parts, Parts 1 and 2, respectively, as shown in Figure 11. In which five dimensions were highlighted for tolerance specification, two dimensions from Parts 1 and 3 from Part 2. Dimensions 1 and 2 confine to the diameter of the protrusions in Part 1, and dimensions 3 and 4 refer to the internal diameter in Part 2, respectively. The Part 2 thickness is governed by the dimension 5.
Step 1: This step involves the preparation of the input file consisting of the geometry and its size attributes along with the dimension. Table 7 illustrates the input details for the two-pin-two-hole assembly and the file was fed to the corresponding network model.
Step 2: The network models were simulated with the input file, and the objective function was set for the GA. A population size of 100 was set for the GA with the aim of minimizing the manufacturing cost.
Step 3: The role of genetic operators was performed in this step in order to identify the best solution for the problem. In this case, a two-point crossover method with a crossover rate of 0.6 and the top mate selection method obtained the best result.
Step 4: The final results obtained from the optimization algorithm is depicted in Table 8.
Two-pin-two-hole assembly.
Input data for the two-pin-two-hole assembly
Two-pin-two-hole assembly results and comparison
Results and discussions
Network model's performance
In conventional mathematical modeling techniques, the accuracy of the result was dependent on the mathematical model developed through curve fitting techniques. Various polynomial equations and exponential and power functions were adopted to correlate the input and output functions. Apparently, different mathematical models yield different results. This paper proposed a new method to model the manufacturing cost–tolerance relation using neural networks and integrated the model to obtain optimum results. Three network models (MLP, BPN, and RBF) were used to train the data set for two clauses. Clause 1 was confined to prismatic parts and clause 2 was assigned for rotational parts. The data sets were fed individually to the network models and trained with the gradient descent method. In the prismatic network model, MLP had a 0.7654 regression correlation coefficient with 0.0197 of fitting error, the BPN model produced a 0.9941 regression correlation coefficient with 0.0054 fitting error, and the RBF model was found with 0.8452 regression correlation coefficient with a fitting error of 0.0091. On the other hand, the rotational network model MLP produced a 0.8972 regression correlation coefficient with 0.0165 error; BPN had a 0.9897 regression correlation coefficient with 0.0094 error and RBF with a 0.7845 regression correlation coefficient with 0.0198 error. In both the clauses, BPN was found very accurate with the maximum regression correlation coefficient and minimum fitting error. This is due to the backpropagation property on the network model, after each learning cycle, the bias analyses the deviation between the input and output variables, and the weight factor for each neuron is updated with the compensation loss function. In addition to it, the gradient descent method analyses the deviation slope from the target position and enables the network models for better learning. Hence, the BPN model could accurately capture the nonlinear relation between the input and output variables.
While analyzing the performance of the network models, the architecture of the models, especially hidden layers, count influenced the total performance. In the BPN model, the learning cycle (epochs) was inversely proportional to the error function. This is due to the change in the weights and the bias after each learning cycle. Hence, the error function decreases with the increased learning cycle. In MLP and RBF network models, the activation function in the hidden and output layers had a great impact on determining the error function. The better regression coefficient (R 2) was achieved in the BPN network. The MLP model was found good during training but produced a poor regression coefficient in subsequent testing and validation. RBF took a long learning time and produced the least coefficient. The best BPN model was assigned as the fitness function and integrated with the GA in order to obtain the optimal values.
Case studies results
The gearbox and the two-pin-two-hole assemblies were solved with the proposed method. In order to validate the proposed method, the result published in the literature was compared. In addition to it, three complex models from the literature, namely combined squared and exponential function model, fifth-order polynomial function model, and concurrent process function model, were solved to claim the efficacy of the proposed method with the existing models. Tables 6 and 8 present the case studies result. The neural network-based cost–tolerance models have performed better than the existing mathematical models, due to the learning ability and function approximation property of the network models. For the first case (gearbox assembly), significant cost saving was observed. As shown in Table 6, the optimized reference manufacturing cost is 132.29 with a saving of 14.25%–17.86%, in addition to it, the tolerance values have also increased considerably. Similarly, for the second case study, the reference optimal manufacturing cost is 295.64 (Table 8), with a saving percentage of 19.97%–34.08%. Simultaneously, the tolerance values have increased significantly. These results serve as an important basis for design and process planning engineers. Network models purely follow the essence of the manufacturing cost–tolerance relation. An increase in tolerance will decrease the manufacturing cost.
Impact of genetic operators
While solving the case studies, the following inferences were drawn during the integration of neural network models with the GA. Figure 12 shows the interaction effects of the crossover and selection process. Among all the interactions, the uniform crossover with the absolute top mate section produced the best result of 132.28. Figure 13 represents the performance of mutation and the crossover rate. Better results were achieved by increasing the crossover rate. The best solution was obtained at a 0.8 crossover rate. In contrast, an increase in the mutation rate produced poor results. The best solution was observed at a 0.1 mutation rate and then the results gradually increased. At a lower rate of mutation, the minimum change in chromosome count leads to an effective child population. While increasing the mutation rate, many chromosomes in the strings of the parent population gets changed and prevents the GA from performing an effective search. Hence, the best mutation rate of 0.1 obtained the optimum result.
Interaction effects of selection and crossover methods.
Effect of mutation and crossover rates.
Major improvements due to the network models
The major improvements in manufacturing cos–tolerance modeling using the neural network models and subsequent optimization of tolerances are as follows:
1. Neural network models made an accurate mapping of the nonlinear cost–tolerance relation of 0.9941 regression coefficient with 0.0054 RMSE, which was not possible through traditional mathematical modeling using curve-fitting techniques.
2. The tolerance specification in the proposed method has considered the geometry and size attributes of a product. Also, the proposed method has quantified the contribution percentage of tolerance value, length, breadth, thickness, and diameter.
3. Neural networks can accurately capture the manufacturing cost–tolerance relation, which is more realistic than the existing models.
4. The integration of the GA with the neural network model proved the versatility of the proposed method in obtaining highly accurate results.
5. The manufacturing cost–tolerance data set can be easily modified to enforce the cost modification during inflation or deflation and makes this method highly versatile.
The primary limitation of the proposed method is the fundamental knowledge of the neural network is essential. The input production data set was limited to a particular range, and still, the range can be expanded. Also, the best method to determine network architecture will be an interesting area of future research.
Conclusion
The proposed method demonstrated the modeling of manufacturing cost–tolerance relationship using neural network models (MLP, BPN, and RBF) and optimizing the tolerance values and manufacturing cost by using the GA. Neural network models were found good in correlating the complex relationship between the tolerance values and its manufacturing cost. It helped to explore the inclusion of the part geometry and its size for a wide production data set. The comparison of the MLP, BPN, and RBF network models performance resulted in important conclusions. MLP provided faster results. BPN was a good network in producing the best regression coefficient value. These network models essentially depend on the production data set, and costly experimentation is not necessary over a period of time. The use of neural networks to aid the design and process planning engineers has introduced a new methodology. This facilitates engineers during the design process and helps them in supporting the technological decision-making process.
A. Saravanan is a researcher in the Department of Production Engineering, National Institute of Technology, Tiruchirappalli. He got his Master of Engineering (M.E.) degree in Manufacturing Engineering from Anna University in 2013, Chennai. He was awarded Bachelor of Technology (B.Tech) degree in Mechanical Engineering from the Vellore Institute of Technology, Vellore during 2009. He obtained his diploma degree in Tool and Die making from Nettur Technical Training Foundation (NTTF). The theme of his dissertation is Ontological Modeling of Geometric Dimensions and Tolerances (GD&T) in the new product development process.
J. Jerald is an Associate Professor in the Department of Production Engineering at the National Institute of Technology, Tiruchirappalli. He received his Ph.D. (2006) from Bharathidasan University, Master of Engineering (1997) from Bharathiyar University and Bachelor of Engineering (1995) from Bharathiyar University. His research interests include Scheduling, Optimization, Micro/Nano Machining processes, and Flexible Manufacturing Systems.
A. Delphin Carolina Rani completed her Ph.D. (2018) at Bharathidasan University, Tiruchirappalli in Computer Science and Engineering. She received her Master of Engineering (2001) from then Shanmugha College of Engineering (now Sastra University) and Bachelor of Engineering (1997) from the Government College of Technology, Coimbatore.
