Design of an intelligent simulator ANN and ANFIS model in the prediction of milling performance (QCE) of alloy 2017A

Abstract

Artificial neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFISs) are machine learning techniques that enable modeling and prediction of various properties in the milling process of alloy 2017A, including quality, cost, and energy consumption (QCE). To utilize ANNs or ANFIS for QCE prediction, researchers must gather a dataset consisting of input–output pairs that establish the relationship between QCE and various input variables such as machining parameters, tool properties, and material characteristics. Subsequently, this dataset can be employed to train a machine learning model using techniques like backpropagation or gradient descent. Once the model has been trained, predictions can be made on new input data by providing the desired input variables, resulting in predicted QCE values as output. This study comprehensively examines and identifies the scientific contributions of strategies, machining sequences, and cutting parameters on surface quality, machining cost, and energy consumption using artificial intelligence (ANN and ANFIS). The findings indicate that the optimal neural architecture for ANNs, utilizing the Bayesian regularization (BR) algorithm, is a {3-10-3} architecture with an overall mean square error (MSE) of 2.74 × 10⁻³. Similarly, for ANFIS, the optimal structure yielding better error and correlation for the three output variables (E_tot, C_tot, and Ra) is a {2, 2, 2} structure. The results demonstrate that using the BR algorithm with a multi-criteria output response yields favorable outcomes compared to the ANFIS.

Introduction

The manufacturing sector is one of the world’s largest consumers of electrical energy. With the increase in the cost of energy and the associated carbon emissions, reducing energy demand has become an urgent challenge for manufacturers in recent years. The machine tool consumes a great deal of electrical energy. With the aim of reducing energy consumption and cost in CNC machining, the selection of optimal machining strategies and cutting parameters is considered one of the most important saving policies. The use of new prediction and optimization techniques with artificial intelligence technology can positively contribute to this economic policy. Several researchers have used artificial intelligence tools to solve prediction and optimization problems in mechanical manufacturing. Ben Yahia et al. [1] have developed an integrated environment for the automated planning of machining processes to fabricate prismatic parts. The system is based on the application of the neural network. The system presented is based on the application of the ANN. The model used in this study is applied to the design of the features, namely pockets, grooves, steps, and essentially their intersections: pocket/pocket, step/pocket, step/step, pocket/groove, step/groove, and groove/groove. Girish and Kuldip [2] used the neural network (NN) to predict energy consumption and surface roughness (Ra). They performed machining experiments to verify the suitability of the proposed model for predicting energy consumption and Ra. The results predicted by the proposed model indicate a good synchronism between the predicted values and the values. Aykut et al. [3] studied the milling Ra of alloy AA6061. An experimental model has been improved to assess surface quality using response surface methodology (RSM) and artificial neural networks (ANNs). Serra et al. [4] used multi-objective optimization by the genetic algorithm (GA) by integrating regression analysis to simultaneously minimize Ra, power consumption, and cutting time and maximize productivity. Tzu-Liang et al. [5] developed a Ra prediction model for a set of input data, namely cutting speed, cutting depth, and feed rate. The model was verified by comparing the fuzzy output (FL) with the experimental data used to build the empirical model. The results of these experiments are in good agreement with those predicted by the fuzzy logic model.

In mechanical manufacturing, machine tools consume energy that can reach critical values. Improving the energy efficiency of machine tools can lead to a significant reduction in the cost of products. Research on reducing energy consumption is still insufficient in view of the increasing use of energy sources [6]. For example, Yansong et al. [7] presented an approach that integrates both Ra and energy consumption to optimize cutting parameters during turning. Ampara and Paul [8] studied how different tool paths can influence the direct energy demand in machining. Therefore, they suggested a way to drastically reduce the energy intensity at the level of material removal. Experimentation demonstrates that the energy consumption of the unidirectional method for the y axis, about 230 kWh, is more than that of the parallel contour, 120 kWh. Resul et al. [9] presented a prediction model to estimate the energy consumption involved in milling prismatic parts. They studied the effect of the cutting strategy on the energy consumed and the total cutting time of the rectangular open pocket feature. Measurements of cutting energy, auxiliary energy, and base energy showed that the “zigzag” cutting strategy consumes the least energy, and the “zig with contour” strategy consumes more energy. Congbo et al. [10] carried out a set of experiments to demonstrate the performance of operational strategies in the milling process. The authors used five tool path strategies in this process, namely bidirectional along x, parallel contour, bidirectional along y, bidirectional at an angle of 45 °, and spiral contour. The results showed that the maximum specific energy consumed (SEC) is given by the strategy of the spiral contour (87 J/mm³). On the other hand, the minimum energy is given by the bidirectional strategy along x (53.1 J/mm³). In the work of Bousnina and Hamza [6], the authors studied the effects of cutting parameters on energy consumption in the turning process of 304-L stainless steel. These studies have shown that the reduction in energy consumption can reach a value of 58.42%. They also showed that the increase in the energy efficiency (EE) of the machine can reach 18.96%.

Few researchers have evaluated optimal cutting conditions based on minimum cost during the manufacturing process. For example, Qiulian et al. [11] used multi-objective optimization by the non-dominated sorting genetic algorithm II (NSGA-II) algorithm oriented toward three objectives and affected by three variables. The three variables are feed rate, depth of cut, and cutting speed. The three goals are energy consumption, minimum machining cost, and better Ra. Congbo et al. [12] studied multi-pass milling face milling and used multi-objective optimization to maximize energy efficiency and minimize production costs by the adaptive multi-objective particle swarm. The results showed that increasing cutting speed, depth of cut, and feed rate simultaneously reduced production time and cost. To achieve energy saving and low cost of CNC machining, Yongmao et al. [13] used a multi-objective optimization approach by integrating the adaptive particle swarm optimization (APSO) algorithm and the improved GA (NSGA-II). Experimental results have shown that the multi-objective optimization model is feasible and efficient and that it can effectively help operators balance energy consumption and manufacturing costs.

Optimizing this process has become a primary stake to reach higher productivity and quality. To optimize process planning, it is important to select a suitable machining strategy [14]. The main objective of this research is to provide a multi-criteria help tool for determining the optimal machining process by integrating the factors: QCE.

The inventory of the main works of research on the optimization of the machining process shows the wide variety of tools and parameters that can influence this process. Table 1 presents these different works. This table shows that these studies are devoted mainly to the definition of simple machining entities (facing, pocket, etc.). On the other hand, most of these studies use some strategies without taking into account the machining ranges (sequences). It was also found that the influence of machining strategies and sequences on the manufacturing cost is nonexistent in all previous studies. On the other hand, the combination of the roughness, cost, and energy output responses is linked only with the cutting parameters and this is for the work of Qiulian et al. [11].

Table 1. The different works presented

Finally, there is no study or model that takes into account cutting parameters, strategies, and machining ranges at the same time for the modeling and optimization of surface quality, machining cost, and energy consumed (QCE) of numerically controlled machine tools to machine interacting entities using artificial intelligence, which will be the subject of this article.

Experimental methods

The main objective of manufacturing industries is to minimize the cost of the finished product as much as possible while maintaining the superior quality of the product. Today, energy consumption has become the main factor that directly influences the cost of machining. Faced with this problem, it is necessary to minimize the energy consumption of machine tools in the machining process. This minimization cannot be obtained without knowing all the machining strategies. The problem gets a bit more complicated when we talk about interacting machining features. Figure 1 depicts aeronautical structural parts that are required for frame construction and are frequently manufactured using numerically controlled machine tools. These parts are high-value critical components full of complex and interactive machining features, for example, hole/pocket and pocket/groove.

Figure 1. Example of interacting machining features of aircraft structural parts [15].

Most researchers who have worked on energy consumption use a single machining feature, for example, pocket and surfacing, with a limited number of tool paths. Under these conditions, it is difficult to measure this consumption since a part can contain several features and these features can interact, which requires several combinations of machining operations. So the contribution in this work is made there, that is, by creating several sequences (ranges) with different machining strategies in order to choose the optimal sequence that gives minimum cost, energy consumption, and roughness. A machining strategy is a methodology used to generate a series of operations to produce a given shape. The choice of these strategies will be to achieve well-determined specifications and shapes. In this context, three machining strategies have been chosen (zigzag, zig, and inward parallel contour (IPC); Figure 2.

Figure 2. Machining strategies.

In this part, the case of pocket/groove features has been studied by illustrating the effects of the planning of machining sequences, machining strategies, and cutting parameters on the surface quality, manufacturing cost, and energy. Figure 3 presents the machining features associated with the selected part. In order to make this part, the machining features will be used to finally obtain a set of combinations of sequences called the “machining range.” Table 2 illustrates all the machining sequences used in this study with the different combinations of strategies (zigzag, IPC, and zig).

Figure 3. Machining features.

Table 2. Machining sequences

Materials and measurements

All the experimental tests are carried out at the workshops at the Higher Institute of Technological Studies of Gabes (ISET Gabes). The machine used is a Realmeca C300H 4-axis machining center. The center generates power between 5.5 kW and 7.5 kW with a maximum rotation frequency of 6500 rpm. This machine is powered by 380 V electrical energy and 6 bar pneumatic energy. The Catia V5 software used in this work makes it possible to create the tool paths and then generate the G-code program compatible with the Num director of the center. The tool used is an uncoated high-speed steel tool with a diameter of 8 mm and two teeth (Figure 4).

Figure 4. Measurement plan.

The material of the machined part is an aluminum alloy (2017A: AlCu4MgSi). This material is widely used in the aerospace, automotive, and so forth industries. This material has high mechanical characteristics after treatment and also good machinability, polishability, and good heat resistance between 100 and 250 °C. Table 3 shows the chemical composition of the material used.

Table 3. Chemical composition of the material (wt%)

A Chauvin-Arnoux CA8332 power analyzer was used in order to measure the power consumed by the machine at each instant during a machining operation. Data processing is performed using the Power Analyzer’s Dataview interface. Figure 5 illustrates the shape of the power consumed during the machining of the S₆ sequence. This graph consists of two main parts. The first part is the machining of the features F₂ with the IPC strategy, which in turn consists of three practically identical parts which correspond to the three layers of the same depth of cut (a_p). Also, note that each layer consists of a pace for a cutting width a_e = tool diameter and a second for a width a_e = 3 mm. This is why the power for the first width is greater than the second. Now for the second part, the tool, after completing the first feature F₂, will move on to execute F₁. During the machining of F₁, the tool, a large part of its trajectory passes empty (without cutting) because a large part of the material has been removed by the feature F₂. For this, the machining phase of this part is practically nonvisual in the shape of the power.

Figure 5. Graph of the power consumed for the sequence S₆.

According to Figure 5, the power consumed can be written in the following forms:

(1) $$ {P}_{pi}={P}_0+{P}_{c\_ pi}\hskip2.28em i=\mathrm{the}\;\mathrm{th}\;\mathrm{layer}\hskip1.68em 1\le i\leqslant 3 $$

(2) $$ {P}_{pi}^{\ast }={P}_0+{P}_{c\_ pi}^{\ast } $$

(3) $$ {P}_g={P}_0+{P}_{c\_g} $$

The arithmetic Ra is measured using a KR100 roughness meter. The stroke measured is 6 mm for a caliber of 2.5 mm. Two studies will be carried out in order to reduce energy consumption, minimize the cost of machining, and increase the surface quality of the machined part. The working method for the first case study consists of carrying out a set of machining sequences with different strategies while keeping the cutting parameters constant, namely cutting speed, feed rate, and depth of cut. This is in order to see the influence of sequences and machining strategies on energy consumption, cost, and surface quality. Following and after the realization of the first case and the prediction of the optimal sequence by the use of gray relational analysis (GRA), an experimental plan with a variation of the cutting parameters on this sequence will be carried out in the second case. The objective, in this case, is to predict the experimental results by the use of artificial intelligence and to determine the effects of the cutting parameters on the output responses. The work plan is shown in Figure 6.

Figure 6. Work plan diagram.

One of the big problems in companies is determining the time and cost of manufacturing a product [16]. In the case of CNC machining, it is also interesting to determine the time and cost of each operation in order to choose the optimal machining sequence which takes into account QCE in its execution. The cost of a machining operation can be estimated by the equation:

(4) $$ {C}_{tot}={C}_{Machine}+{C}_{Tool}+{C}_{Energy} $$

(5) $$ {C}_{Machine}={\mu}_1+{t}_{cycle}.{\mu}_2 $$

(6) $$ {C}_{Tool}=\varepsilon\;\frac{t_c}{T} $$

(7) $$ {C}_{Energy}=\delta\;{E}_{tot} $$

Results and discussion

CNC machines are the most important means of production in the manufacturing industry that consumes a large amount of energy during a machining operation. A presentation of the results of the two case studies will be carried out in this part.

First case

The first case study focuses on the variation of machining strategies and sequences by setting the cutting parameters for all the tests. The choice of technological machining parameters was made taking into account the catalog of the tool manufacturer and the capacity of the machining center. Table 4 presents the cutting parameter values used in this first part. This study takes into consideration the machining sequences and strategies (tool paths) in order to obtain the optimal sequence. Table 5 illustrates the values of energy consumed, cost, and roughness. Table 6 presents the energy consumed for feature F1 for the different strategies (IPC, zigzag, and zig). Figure 7 illustrates the effects of each strategy for this feature F₁ on the energy consumed (E_tot). The figure shows that the IPC strategy admits minimum energy consumption compared to the other two. The maximum energy consumption for F₁ is achieved with the zig strategy. This increase in energy for this strategy means that the cut is done in one direction and that the tool for a significant part of its cycle moves in the air. This conclusion converges with the results of Edem et al. [17] and Altıntaş et al. [18]. Figure 8 illustrates graphs of energy consumed and machining cost. The figure shows that the two graphs follow the same variation, which proves that the energy consumed has a significant influence on the cost. As a result, good energy policy management in industries allows for cost reductions in manufacturing. On the other hand, the sequence S₈ = F₁-F₅-F₆ has the minimum cost and energy. This sequence is characterized by the fact that the tool along its trajectory is in full material (cutting phase). In other words, the tool along its trajectory does not cross empty areas (without material). This condition saves a significant amount of cutting time. On the other hand, the S₈ sequence is realized by the IPC strategy for all the features F₁-F₅-F₆, which proves that the choice of the tool path and the machining sequence has a significant influence on the cost and energy.

Table 4. Cutting parameters (first case)

Table 5. Experimental values (first case)

Table 6. The energy consumed for machining the feature (F₁) with the different strategies (first case)

Figure 7. Histogram of the energy consumed for feature (F₁) with the different strategies.

Figure 8. Energy and cost graphs for all sequences.

Industry and researchers face a big challenge when they try to study the surface quality of machined parts. Most researchers who have worked on surface quality as a function of the tool path have used a single machining feature in their studies. Examples of this claim are the work of Zaleski et al. [19] and Ali Raneen et al. [20]. Indeed, the use of interacting features with a set of tool paths can lead to logic of the choice of surface quality. On the other hand, an overlay of tool paths when machining Fi features can modify the surface texture of the machined part.

Figure 9 shows the Ra of successive machining of F₁-F₂ entities for sequences S₁, S₅, and S₇ with IPC-IPC, zigzag-IPC, and zig-IPC strategies, respectively. The figure shows that machining F₁ and then F₂ (F₁-F₂) with zig-IPC strategies has the lowest roughness. According to the references by Aramcharoen et al. [21] and Ali Raneen et al. [20], the zig strategy for machining a single feature has the maximum roughness compared to the IPC strategy, which has the lowest roughness. In this study, the problem is a little different since the tool for the first feature F₁ creates several passes with the same strategy in order to complete the depth h of the part. Then, the tool will switch to executing F₂ with another strategy. The problem occurs in the last pass for feature F₂. Indeed, the tool causes the last pass with this new strategy, which passes over the texture left by the first strategy of the feature F₁. This phenomenon can cause a superfinish in the F₁ area. This is possible when the first strategy has a poor surface quality compared to the second strategy. The conclusion of Aramcharoen et al. [21] that there is a synergy between the roughness and the energy consumed is not valid in this study because the problem is more complicated given that the tool makes trajectories in the air (without cutting), which can disturb this conclusion, which is not the case in the studies by Aramcharoen et al. [21] and Ali Raneen et al. [20]. The next step is to determine the optimal sequence S_i, which gives minimum energy consumption, machining cost, and Ra.

Figure 9. Surface roughness histogram of F₁-F₂ features made with IPC-IPC, zigzag-IPC, and zig-IPC strategies.

Multi-objective optimization by GRA

After carrying out the experimental tests for this first case, it is now necessary to determine the optimal machining sequence. In this study, there are three output responses, namely energy consumed, cost, and roughness. In this case, it is necessary to have a tool capable of solving this multi-criteria optimization problem. GRA helps to solve this type of uncertainty problem given its ability to understand uncertain systems with partially known information [22]. This theory was established by Deng in the late 1990s. The procedure required by this theory is presented as follows [20]: To obtain better surface quality, minimum cost, and low power consumption, the condition “the lower the better” will be chosen.

(8) $$ {x}_i=\frac{\mathit{\max}{y}_i(k)-{y}_i(k)}{\mathit{\max}{y}_i(k)-\mathit{\min}{y}_i(k)} $$

where $ {x}_i $ is the output response after normalization and $ {y}_i(k) $ is the experimental values of the output responses. The largest and smallest values are $ \max \left({y}_i(k)\right) $ and $ \min \left({y}_i(k)\right) $ , respectively.

After normalization, the next step is devoted to the calculation of the gray relational coefficient (GRC). The following equation presents this coefficient:

(9) $$ {\psi}_i=\frac{\Delta_{min}+\phi\;{\Delta}_{max}}{\Delta_{0i}(k)+\phi\;{\Delta}_{max}} $$

where $ {\Delta}_{0i}(k) $ represents the absolute value of the deviation between the test reference $ {y}_0(k) $ and $ {y}_i(k) $ , $ {\Delta}_{0i}(k)=\left\Vert {y}_0(k)-{y}_i(k)\right\Vert $ . $ {\Delta}_{min} $ and $ {\Delta}_{max} $ respectively represent the minimum and maximum value of $ {\Delta}_{0i}(k) $ . $ \phi $ represents the distinctive coefficient which includes the interval [0,1]. In this work, the coefficient $ \phi $ is 0.5.

The next step is to figure out the gray relational grade (GRG) after figuring out the GRC.

(10) $$ {\gamma}_i=\sum \limits_{k=1}^n{\omega}_k{\psi}_i $$

where $ {\omega}_k $ denotes the normalized weight of the kth experimental response.

In the methodology of GRA, the maximum value of $ {\gamma}_i $ indicates that the input parameters associated with this value are close to the optimum [23]. In this work and according to Table 7, the maximum value of $ {\gamma}_i $ corresponds to the sequence S₈. This sequence shows the best way to combine the input parameters, taking into account their different weights. In this first study, the cutting parameters are constant for all the tests, so the combination F₁-F₅-F₆ with the same IPC machining strategy is the optimal combination.

Table 7. Gray relational grade (GRG) (first case)

In what follows, the study relates to this sequence S₈ with the combination F₁-F₅-F₆.

Second case

In this second part, the objective is to determine the effects of the cutting parameters on the output variables, E_tot, C_tot, and Ra. Predicting experiment results has been done by using neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFISs). The last phase of this second part is a comparison between the two artificial models in order to choose the model that gives more refined results. The cutting parameters associated with this part are shown in Table 8.

Table 8. Cutting parameters (second case)

The depth of cut (a_p) is chosen to ensure that for each level, the tool removes the same depth. The total cutting height of the part is h = 1.5 mm. Table 9 presents the experimental values of the 15 trials of E_tot, C_tot, and surface quality for the machining of the S₈ sequence with a different combination of cutting parameters.

Table 9. Experimental values (second case)

Prediction with ANN

ANN models are programming techniques that simulate the human brain [24]. These models have been implemented in several manufacturing, scheduling, and other industry applications [25]. An ANN is a digital adoption composed of manipulation (processing) elements called neurons. Neurons form a complex random system that generates a relationship between input parameters and output variables. Nonlinear regression analysis of network output responses [26] is used to figure out how well neural network-based predictions work. In general, NN consists of three layers, input layers, hidden layers, and output layers.

Two proposals for neural architecture were presented in this study in order to determine the structural performance of a neural network. The first architecture consists of three inputs (V_C, f, and a_p) and three outputs (E_tot, C_tot, and Ra) at the same time (Figure 10a). The second consists of three inputs and a single output presented by the networks ANN1, ANN2, and ANN3 (Figure 10b).

Figure 10. Proposed neural architectures.

The objective of this study is to determine the optimal structure at the output level, number of hidden neurons, and level of the learning algorithm used. The performance of all structures is measured using the MSE during the algorithm learning process. The MSE is given by the following equation:

(11) $$ MSE=\frac{\sum \limits_{i=1}^n{\left({x}_i-{y}_i\right)}^2}{n} $$

The second performance criterion is the correlation coefficient (R²). The R² varies between −1 and + 1. R² close to +1 indicates a strong positive linear relationship between input parameters and output variables [27]. The R² coefficient is calculated from this equation:

(12) $$ {R}^2=1-\left(\frac{\sum \limits_{i=1}^n{\left({x}_i-{y}_i\right)}^2}{\sum \limits_{i=1}^n{y_i}^2}\right) $$

Several learning algorithms use backpropagation in their processing systems to determine the weights and biases of neural structures. Figure 11 presents the general NNarchitecture with the different parameters.

Figure 11. General neural network architecture.

For structural NN modeling, the Levenberg-Marquardt (LM) algorithm, the scaled conjugate gradient (SCG) algorithm, and the BR algorithm were used. The present work uses the sigmoid function as an activation function in order to normalize the output response. The activation function is represented by the following equation:

(13) $$ f\left({p}_i\right)=\frac{2}{1+{e}^{-2{p}_i}}-1 $$

where p is the input conversion function.

For all neural architectures, the data are divided into three groups: learning, testing, and validation. Seventy percentage of the data is devoted to the learning phase, 15% to the testing phase, and finally 15% to validation. Table 10 shows how to figure out the best learning algorithm, the number of hidden layers, and the number of best outputs. After several tests, the optimal architecture in this study for a single output is {3-10-1} for the output variable E_tot and {3-14-1} for the variables C_tot and Ra. The same LM learning algorithm is used to realize all optimal structures. The optimal architecture with three outputs (E_tot, C_tot, and Ra) is now presented by the {3-10-3} architecture realized with the BR algorithm. The backpropagation algorithm was very good at predicting the amount of energy used, the cost of machining, and the quality of the surface. Figure 12 illustrates the predicted values of E_tot, C_tot, and Ra compared to the experimental values for the single output structure. The R² for Etot, Ctot, and Ra are 0.9984, 0.9963 and 0.8741, respectively. These values show a good correlation between the predicted values and the experimental values. On the other hand, the MSE for the output responses is low, namely 8.25 10⁻⁶ (kWh), 1.42 TD (0.44 $), and 1.17 10⁻⁴ μm, respectively, for E_tot, C_tot, and Ra. Figure 13 shows the predicted values of Etot, Ctot, and Ra versus the experimental values for the three-lead structure. The R² for Etot, Ctot, and Ra are 0.9992, 1, and 0.9117 respectively. So, from Table 10 and Figures 12 and 13, the conclusion is drawn that the LM algorithm has good learning with a single output response. On the other hand, the BR algorithm has good learning with a multi-criteria response (three for this work). By comparison between these architectures, the {3-10-3} architecture with the BR algorithm has a good correlation compared to the other architectures. The MSE global MSE for this architecture is 2.74 10⁻³. Therefore, the use of artificial intelligence by neural networks seems to be a useful methodology to simulate multi-criteria responses in mechanical manufacturing. In what follows, the {3-10-3} architecture will be retained.

Table 10. Different neural architectures (second case)

Figure 12. Experimental values versus predicted values (single output: {3-10-1} and {3-14-1}).

Figure 13. Experimental values versus predicted values (three outputs: {3-10-3}).

Prediction with ANFIS model

The ANFIS model is highlighted to predict experimental results in different fields of engineering [28, 29 and 30]. ANFIS is a hybrid fuzzy inference approach from Sugeno [31] which simultaneously combines a fuzzy inference system (FIS) with a NN. This combination aims to make the system efficient in order to solve complex problems [32]. In the general case, the ANFIS model includes five consecutive treatment lines. The lines (layers) are connected to each other by different nodes. Each entry node is drawn from the previous line. Figure 14 presents the general architecture of the ANFIS model. The numerical interpretation of this architecture can be presented as follows:

Rule 1 = if x is A₁ and y is B₁, then f₁ = p₁ x + q₁ y + r₁

Figure 14. General architecture of the ANFIS model.

Rule 2 = if x is A₂ and y is B₂, then f₂ = p₂ x + q₂ y + r₂

where x and y are the input parameters of the experimental study, and p_i and q_i represent the variables of the fuzzy set. The output function of the ANFIS model is presented by

(14) $$ f=\overline{w_1}{f}_1+\overline{w_2}{f}_2 $$

where $ \overline{w_1}=\frac{w_1}{w_1+{w}_2} $ ; $ \overline{w_2}=\frac{w_2}{w_1+{w}_{2.}} $

where w_i is the trigger strength for each rule.

In this present work, in order to find the optimal architecture of the ANFIS model, a combination of numbers and types of membership functions (MFs) (Gaussian-shaped MFs, gaussmf and gauss2mf, and triangular-shaped MF, trimf) was carried out. The MFs used in this work are the trimf, gaussmf, and gauss2mf. The numbers of MF used are {2 2 2}, {2 2 3}, and {2 3 3}. The MF of constant and linear types is used for the output variables. The ANFIS modeling process runs with 75% of the data for training and 25% for testing. In this process, the iteration number for the mapping is equal to 100. Table 11 presents the different combinations of ANFIS architecture with the different MFs. According to this table, structure {2 2 2} is the optimal structure for the three output responses (E_tot, C_tot, and Ra). According to the results, the function (trimf) has the lowest test error for the energy consumed (E_tot) with a linear output. On the other hand, the (gaussmf) function has the lowest error for C_tot and Ra output responses with constant and linear output functions, respectively. The MSE_All values for the E_tot, C_tot, and Ra output responses are 0.01913, 3.399 and 4.516 E-3, respectively. Figure 15 illustrates the final {2 2 2} architecture for the three output variables. Figure 16 illustrates the comparison between predicted and experimental values for output responses. The R² values for the variables E_tot, C_tot, and Ra are 0.95, 0.965 and 0.968, respectively. These values present a good correlation but are less weak than those of the neural network, except for the surface quality for the ANFIS model, which is greater than that of the ANN (0.968 > 0.9117). Table 12 shows a comparison between the two ANN and ANFIS models’ global MSEs (training and testing) for the different output variables. The result shows that the global MSE of the {3-10-3} neural structure is lower compared to that of the ANFIS model. Indeed, Figures 12 and 13 (ANN), Figures 15 and 16 (ANFIS), and comparison Table 12 show that the use of the BR algorithm with a multi-criteria output response can give good results when compared with ANFIS.

Table 11. Different combinations of ANFIS architecture (second case)

Figure 15. Final {2 2 2} architecture.

Figure 16. Experimental values versus predicted values (ANFIS model).

Table 12. The MSE_ALL values of the ANN and ANFIS models (second case)

A 3D surface plot study was carried out in order to describe the effects of the cutting parameters on the output responses. Figure 17 shows the variation of energy consumed (E_tot), cost (C_tot), and surface quality as a function of the cutting parameters. Figure 17a and 17b shows that for a decrease in the feed rate (f), there is an increase in the energy (E_tot) and the cost (C_tot). This conclusion is because the machining time decreases when the feed rate increases, which positively influences the energy consumption and the cost. This conclusion is similar to the studies of references [33, 34 and 35]. Figure 17e shows that as the feed rate increases, the surface quality decreases. In other words, the roughness (Ra) increases. Indeed, the feed rate (f) has a remarkable influence on the surface quality compared with the cutting speed. In this present work, the depth of cut (a_p) is chosen so that all levels have the same depth of cut for a height of cut h. Figures 17(b) and (d) clearly show that as the depth of cut increases, so does the energy (E_tot) and the cost (C_tot). The decrease in the number of cutting levels, caused by an increase in the depth of cut, leads to a reduction in total machining time. Similarly, for the surface quality, the increase in the depth of cut has a negative influence on the roughness (Ra) (Figure 17(f)). This is because the tool tends to vibrate more as the depth of cut gets deeper, especially if the diameter of the tool is small. These conclusions converge with the studies of Khan Aqib et al. [35], Eser et al. [36] and Devarajaiah et al. [37].

Figure 17. 3D surface plot of energy (E_tot), cost (C_tot), and roughness (Ra).

Development of an intelligent simulator based on prediction models ANN and ANFIS

An interactive interface has been developed to help machinists predict the energy consumed, surface quality, and cost of a 2017A alloy part containing an interacting pocket and groove. The simulator was implemented using the “Guide” interface of the MATLAB 2016 software. Figure 18 shows this user interface named “QCE_Intelligent_simulator,” which is simple and extremely easy to learn. As shown in the figure, the user must first input the values of the cutting parameters (Inputs), that is, the cutting speed (V_c), the feed rate (f), and the depth of cut (a_p). Subsequently, the user has the choice to predict the results according to the ANN model or the ANFIS model by pressing the “Predict” button.

Figure 18. QCE_Intelligent_simulator.

The Catia-machine interaction is achieved through the production of a G-code program according to the ISO 6983 standard compatible with the CNC director Num of the machining center. The power is measured in real time during the execution of the machining operation. The actual results are compared to what was expected after the data and results have been analyzed [38, 39]. When another operation is executed, the machining parameters are updated.

Comparative analysis

A very few of the researchers have applied artificial intelligence models (ANN and ANFIS) to optimize machining performance in milling. We cite, as examples, works somewhat close to our study: Pourmostaghimi et al. [40] propose a model-based smart optimization methodology to optimize the production cost and material removal rate under surface quality constraint during a turning operation in hardened AISI D2. They determine the optimal machining parameters by applying the particle swarm optimization (PSO) algorithm. Namlu et al. [41] developed an ANN model in the Python programming environment to predict the cutting forces of Ti–6Al–4 V machining. The results showed that the experimental cutting forces were estimated with a successful prediction rate of 0.99 with mean absolute percentage error and root MSE of 1.85% and 13.1, respectively. Pourmostaghimi et al. [42] proposed a novel PSO-RDNN hybrid approach combining PSO algorithm with recurrent dynamic neural network (RDNN), for multi-performance optimization of machining parameters in finishing turning of AISI D2 hardened parts. The proposed methodology returns a Pareto optimality plot, which represents cutting variables optimized for several different cutting conditions.

The work of Sada and Ikpeseni [43] is the only research closest to our work and which can be compared with the results of our work even if the materials are not the same. Sada and Ikpeseni provide valuable insights into the predictive performance of ANNs and ANFISs for predicting the machining performance of AISI 1050 steel. This study focuses on a specific application and evaluates the modeling ability of both ANN and ANFIS models. In this research, the authors likely conducted experiments or collected data related to the machining process of AISI 1050 steel. They then compared the predictive capabilities of ANN and ANFIS models by training and testing them on the collected data. The evaluation criteria could include accuracy, precision, recall, mean absolute error, or other relevant performance metrics. Sada and Ikpeseni assess the performance of ANN and ANFIS models in predicting machining responses (metal removal rate and tool wear) in an AIS steel turning operation. The R² obtained from the analysis further confirms the preference of ANN with a maximum value of 92.1% recorded using ANN compared to that of ANFIS of 73%. Based on their analysis and comparison, the authors found that the NN models (ANN) exhibited superior predictive performance over the ANFIS models. This conclusion aligns with your statement that the authors of reference [43] established the predictive superiority of neural networks over ANFIS. The study’s findings suggest that ANN models were better at capturing the intricate relationships and patterns in the machining performance data of AISI 1050 steel. These NN models likely outperformed ANFIS models in terms of accuracy and generalization capability.

In our work, we obtained the R² values for E_tot, C_tot, and Ra: 99.92%, 100%, and 91.17%, respectively, for the ANN model and 95%, 96.5%, and 96.8%, respectively, for the ANFIS model. In our article, we observed a strong correlation between the results, highlighting the superiority of the ANN model over the ANFIS model in all instances, which aligns with the findings of Sada and Ikpeseni [43].

The obtained R₂ in your work demonstrate the superior predictive performance of the ANN model compared to the ANFIS model for the variables E_tot, C_tot, and Ra. The high R² values achieved by the ANN model, such as 99.92% for E_tot, 100% for C_tot, and 91.17% for Ra, indicate a strong correlation between the predicted values and the actual values. The superior predictive performance of the ANN model compared to the ANFIS model, as evidenced by the high R₂ obtained in our work, can be attributed to several scientific factors. NNs, including ANNs, excel at capturing and representing nonlinear relationships in data due to their flexible and adaptable nature. They can adjust their internal parameters during training, optimizing their performance and enabling them to model complex nonlinear dependencies more effectively than ANFIS models. Additionally, the end-to-end learning capability of neural networks allows them to learn directly from raw input data without manual feature engineering, extracting relevant features and uncovering hidden patterns. The scalability and depth of neural networks, particularly in deep architectures, enable them to handle intricate and high-dimensional datasets, contributing to their superior predictive power. These scientific factors collectively justify the superior predictive performance of the ANN model in our work.

Conclusion

The increase in the world’s population promotes an increased demand for products, which requires enormous energy consumption in industries. In order to evaluate the trade-offs between cut quality, manufacturing cost, and energy consumption (QCE). This article presents an approach that integrates ANNs and ANFIS to predict the effects of strategies, machining sequences, and cutting parameters on the consumption of energy, machining cost, and Ra. Two in-depth case studies were carried out to understand the effects of the parameters introduced into the multi-criteria output responses. Based on the results already found, the studies first show that the strategies and the planning of the machining sequences have a remarkable influence on the energy consumption, the cost of machining, and the surface quality of the parts. In this work, a multi-objective optimization based on the GRA was proposed, which is applied to optimize the sequences and strategies of machining on a part that contains interacting entities. The results obtained confirm that the proposed optimization method is a very indispensable tool for multi-criteria optimization. The use of a variety of architectures and a variety of learning algorithms for the construction of neural networks allows us to increase the range of choice and the rigorous selection of the optimal solution (architecture + algorithm). The {3-10-3} architecture with the BR algorithm is the optimal neural architecture that yields an overall MSE of 2.74 × 10⁻³. Similarly, for the ANFIS, the optimal structure which gives a better error and better correlation is the {2 2 2} structure, and this for the three output variables (E_tot, C_tot, and Ra). Studies also show that for a decrease in the forward speed (f), there is an increase in E_tot and C_tot. In contrast to energy and cost, a decrease in f causes a decrease in Ra.

Future work will aim to extend multi-criteria output responses to account for other factors (e.g., dimensional error and vibration). Finally, an application to a wider range of prediction and optimization with other methods of artificial intelligence can contribute positively to the desired performance.