# Drilling Process of GFRP Composites: Modeling and Optimization Using Hybrid ANN

## Abstract

**:**

## 1. Introduction

_{2}from manganese mine tailings [13]. Response surface methodology (RSM) was used to characterize the influential parameters on the flotation behavior of a sulfurized mixed copper ore [14] and to optimize the grinding process parameters of phosphate ore, to minimize the slimes during production [15].

## 2. Material and Methods

_{d-out}), shown in Table 4, was evaluated by:

_{d}is the delamination factor, D

_{0}is the hole nominal diameter of 6 mm, and D

_{max}is the maximum delaminated diameter that can be drawn from the center point of D

_{0}.

#### 2.1. Artificial Neural Network Models

#### 2.2. Particle Swarm Optimization

_{i}, the particle position updated is a new position, ${x}_{i}^{k+1}$.

_{1}and r

_{2}are random numbers, c

_{1}and c

_{2}are the acceleration coefficients, and k stands for the iteration number. Then, Equation (5) is used to calculate the new position of the particle.

#### 2.3. ANN–PSO Model

## 3. Results and Discussion

#### 3.1. Effect of Drilling Parameters on the Responses

^{2}) value of each estimated model. To the adequacy of the obtained mathematical models, the 3D surface plots constructed by them can be used for predicting the responses for any combination of the machining parameters.

_{d-out}shown in Figure 2, plotted using the obtained quadratic equation, can be used for estimating the F

_{d-out}values for any appropriate combination of the machining parameters: f, N, and t. Figure 2 illustrates that the delamination factor increases with the increase in the feed and decreases with the increase in the spindle speed. It is noticed that with the decrease in laminate thickness, the F

_{d-out}increases. The effect of the feed can be explained: as the feed is increased, the area of the chip increases, where resistance to the cutting of the material is higher. Therefore, large efforts are required to remove the chip [35]. Moreover, Figure 2 elucidates that as the thickness increases, the delamination factor decreases.

#### 3.2. Prediction of Responses by ANN–PSO Model

_{d-out}in the space of this study. The ANN–PSO model learns the relationship between the process control factors (feed, spindle speed, and workpiece thickness) and responses.

_{d-out}under diverse combinations of drilling parameters.

^{2}, of 0.9967, for torque, is higher than that of ANN–PSO for the delamination factor, which is 0.9582. Moreover, the traditional training technique (Levenberg–Marquardt algorithm) was used and appeared to possess lower accuracy than the ANN–PSO model.

_{d-out}, respectively, using the proposed ANN–PSO models. These 3D plots elucidate that the developed ANN–PSO models can interpret the data well and serve as an efficient prediction tool for the torque and F

_{d-out}produced during the drilling process of WGFRE. Thus, it facilitates the exploitation of artificial intelligence in the manufacture of FRP.

#### 3.3. Comparison of Obtained Predictive Models

_{d-out}. Table 8 illustrates the statistical measures of both prediction models: R

^{2}, MSE, and MAPE. From the plots in Figure 7 and the performance measures in Table 8, it was found that the two models can, acceptably, draw and describe the experimental results.

_{d-out}by the ANN–PSO model is 3.55% and 2.52%, respectively, while by the RSM model, it is 9.25% and 3.58%, respectively, as shown in the figure.

#### 3.4. Optimizing Responses

^{2}value has been improved, from 0.993 for the same model to 0.9967 for the artificial neural network model trained using the POS optimization algorithm. With this small improvement, however, the values of the APE were clearly different between the two models, as shown in Figure 8a.

^{2}, which increased from 0.864 with RSM to 0.9582 with ANN–PSO. This makes us say that the neural network model is more capable of describing and evaluating the experimental results, and this is evident in Figure 5 and Figure 8b.

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Surface plot of push-out delamination factor (F

_{d-out}) versus feed, spindle speed, and sample thickness from RSM model.

**Figure 4.**Regression plot between experimental and predictive results of ANN–PSO models: (

**a**) torque (N·cm) and (

**b**) delamination factor.

**Figure 5.**The 3D surface plots of push-out delamination factor (F

_{d-out}) versus feed and spindle speed, at sample thickness of 2.6 mm of drilled samples, obtained by ANN–PSO model.

**Figure 6.**The 3D surface plots f torque versus Feed and spindle speed, at three deferent thicknesses obtained by ANN-– model.

**Figure 7.**Comparison between experimental and predicted results by proposed models for (

**a**) torque (N·cm) and (

**b**) push-out delamination factor.

**Figure 8.**Absolute percentage error (APE) in the prediction of proposed models for (

**a**) torque and (

**b**) F

_{d-out}.

Materials of Used Drill | Geometries | ||
---|---|---|---|

Material Grade | K200 | D (mm) | 6 |

ISO Code | K20~K40 | Flute Length (mm) | 28 |

Tungsten carbide (WC) | 90% | Overall Length (mm) | 66 |

Cobal (Co) | 10% | Helix Angle | 30° |

Grain Size (µm) | 0.5~0.8 | Rake Angle | 30° |

Density (g/cm^{3}) | 14.4 | Clearance Angle | 12° |

Hardness (HRA) | 91.3 | Point Angles | 100° |

Rupture Strength Transverse (MPa) | 3920 | Chisel Edge Length (mm) | 0.3 |

KIC (MPa·m^{1/2}) | 10.5 |

Factors | Levels | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

Feed, f (mm/r) | 0.025 | 0.05 | 0.1 | 0.2 |

Spindle speed, N (rpm) (Cutting speed, m/min) | 400 (7.5) | 800 (15) | 1600 (30) | - |

Sample thickness, t (mm) | 2.6 | 5.3 | 7.7 | - |

Spindle Speed, N (rpm) | Feed, f (mm/r) | Thickness, t (2.6 mm) | Thickness, t (5.3 mm) | Thickness, t (7.7 mm) |
---|---|---|---|---|

400 | 0.025 | 17.76 | 26.10 | 22.75 |

0.05 | 21.70 | 29.08 | 28.81 | |

0.1 | 26.33 | 33.39 | 35.07 | |

0.2 | 30.04 | 41.19 | 43.74 | |

800 | 0.025 | 16.13 | 24.74 | 21.09 |

0.05 | 20.35 | 27.34 | 25.12 | |

0.1 | 24.33 | 31.85 | 33.17 | |

0.2 | 28.58 | 39.69 | 41.56 | |

1600 | 0.025 | 14.83 | 22.08 | 19.91 |

0.05 | 19.19 | 25.06 | 24.21 | |

0.1 | 23.10 | 31.45 | 30.22 | |

0.2 | 27.10 | 37.07 | 39.64 |

Spindle Speed, N (rpm) | Feed, f (mm/r) | Thickness, t (2.6 mm) | Thickness, t (5.3 mm) | Thickness, t (7.7 mm) |
---|---|---|---|---|

400 | 0.025 | 1.39 | 1.38 | 1.41 |

0.05 | 1.42 | 1.39 | 1.44 | |

0.1 | 1.45 | 1.39 | 1.50 | |

0.2 | 1.49 | 1.43 | 1.57 | |

800 | 0.025 | 1.42 | 1.39 | 1.39 |

0.05 | 1.49 | 1.41 | 1.42 | |

0.1 | 1.49 | 1.44 | 1.47 | |

0.2 | 1.58 | 1.45 | 1.54 | |

1600 | 0.025 | 1.35 | 1.32 | 1.37 |

0.05 | 1.41 | 1.40 | 1.40 | |

0.1 | 1.48 | 1.43 | 1.43 | |

0.2 | 1.60 | 1.50 | 1.52 |

Source | Degree of Freedom | Torque (N·cm) | p-Value | F_{d-out} | p-Value |
---|---|---|---|---|---|

f (mm/r) | 3 | 65.48% | 0.000 | 64.22% | 0.000 |

N (rpm) | 2 | 3.77% | 0.000 | 2.82% | 0.160 |

t (mm) | 2 | 27.08% | 0.000 | 12.81% | 0.001 |

Residual/ Error | 28 | 3.67% | 20.05% | ||

Total | 35 |

Coeff. Values | ||
---|---|---|

Coeff. | T | F_{d-out} |

B_{0} | 2.504821562361 | 1.4573630529957 |

B_{1} | 118.92109172956 | 0.94650108016652 |

B_{2} | −0.0059756624435889 | 0.00014598690410596 |

B_{3} | 7.3417239905438 | −0.06642819426032 |

B_{11} | −335.5708004779 | −2.1115459976105 |

B_{22} | 0.000002076953125 | −6.7491319444444 × 10^{−8} |

B_{33} | −0.62808747881869 | 0.0073693566932946 |

B_{12} | −0.0015827267080745 | 0.00040208364389234 |

B_{13} | 9.2268980164296 | −0.015652138293372 |

B_{23} | −0.0001833230469607 | −0.00001008312417709 |

R^{2} | 0.993 | 0.864 |

Model | Network Structure | Mean Square Error | R-Value (R^{2}) |
---|---|---|---|

Torque | 3-6-1 | 0.18 | 0.99835 (0.9967) |

F_{d-out} | 3-6-1 | 0.16968 × 10^{−}³ | 0.97892 (0.9582) |

RSM | ANN–PSO | |||||
---|---|---|---|---|---|---|

Model | R^{2} | Mean Square Error | Mean Absolute Percentage Error | R^{2} | Mean Square Error | Mean Absolute Percentage Error |

Torque | 0.993 | 1.4277 | 9.249 | 0.9967 | 0.18 | 3.5487 |

F_{d-out} | 0.864 | 0.55 × 10^{−3} | 3.5768 | 0.9582 | 0.17 × 10^{−3} | 2.5223 |

Condition | Goal | Lower Limit | Upper Limit | Importance |
---|---|---|---|---|

Feed, f (mm/r) | In range | 0.025 | 0.2 | 3 |

Spindle speed, N (rpm) | In range | 400 | 1600 | 3 |

Laminate thickness, t (mm) | In range | 2.6 | 7.7 | 3 |

F_{d-out} | minimize | 1.3215 | 1.60117 | 4 |

Torque | minimize | 14.8337 | 43.7449 | 2 |

Number | N | f | t | F_{d_out} | Torque | Desirability |
---|---|---|---|---|---|---|

1 | 1600.000 | 0.025 | 5.433 | 1.323 | 21.968 | 0.906 |

2 | 1599.998 | 0.025 | 5.413 | 1.323 | 21.959 | 0.906 |

3 | 1599.997 | 0.025 | 5.452 | 1.323 | 21.977 | 0.906 |

4 | 1599.997 | 0.025 | 5.486 | 1.323 | 21.991 | 0.906 |

5 | 1599.990 | 0.025 | 5.366 | 1.324 | 21.935 | 0.906 |

6 | 1599.999 | 0.025 | 5.317 | 1.324 | 21.908 | 0.906 |

7 | 1599.997 | 0.025 | 5.559 | 1.323 | 22.016 | 0.906 |

8 | 1599.998 | 0.025 | 5.583 | 1.323 | 22.022 | 0.905 |

9 | 1599.999 | 0.025 | 5.237 | 1.324 | 21.856 | 0.905 |

10 | 1599.999 | 0.025 | 5.210 | 1.324 | 21.836 | 0.905 |

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**MDPI and ACS Style**

Abd-Elwahed, M.S.
Drilling Process of GFRP Composites: Modeling and Optimization Using Hybrid ANN. *Sustainability* **2022**, *14*, 6599.
https://doi.org/10.3390/su14116599

**AMA Style**

Abd-Elwahed MS.
Drilling Process of GFRP Composites: Modeling and Optimization Using Hybrid ANN. *Sustainability*. 2022; 14(11):6599.
https://doi.org/10.3390/su14116599

**Chicago/Turabian Style**

Abd-Elwahed, Mohamed S.
2022. "Drilling Process of GFRP Composites: Modeling and Optimization Using Hybrid ANN" *Sustainability* 14, no. 11: 6599.
https://doi.org/10.3390/su14116599