# Combining Artificial Neural Network and Response Surface Methodology to Optimize the Drilling Operating Parameters of MDF Panels

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Experiments

_{T}consumed by the spindle motor, and the other three were dedicated to the forces in the feed movement direction of the drill bit, measured by the three force transducers.

_{T}comprises both the power consumed for idle running P

_{0}and the power consumed for actual drilling P

_{D}, while the sum of the values recorded by the force transducers represents the thrust force F

_{T}.

_{T}and the thrust force F

_{T}were taken into account.

_{T}, and using Equation (1), the variation in the drilling torque T

_{D}was obtained [35].

_{D}is the active power consumed only for drilling, P

_{D}= P

_{T}—P

_{0}, in W;

_{0}is the active power consumed for idle running (average of measured values at idle running), in W; and

_{d}[2]. D

_{max}is the diameter of the circumscribed circle of the delaminated area and the average diameter of the hole D was calculated based on two values measured with the caliper D

_{1}and D

_{2}(Figure 2c).

#### 2.2. Data Modeling

#### 2.2.1. ANN Model Development

_{1}), delamination factor at outlet (Y

_{2}), thrust force (Y

_{3}), and drilling torque (Y

_{4}).

^{2}), mean square error (MSE), mean absolute error (MAE), root mean square error (RMSE), and so on. However, in this work, the designed ANN models were evaluated through correlation coefficient (Equation (3)) and coefficient of determination (Equation (4)), due to the fact that they are the most used statistical indicators in data modelling [38,39,40]. Moreover, the predicted values were plotted against experimental data, according to the approach presented in other studies [18,36].

_{i}is the experimental value, p

_{i}is the predicted value, $\overline{\mathrm{a}}$ is the mean of the experimental values, and $\overline{\mathrm{p}}$ is the mean of the predicted values.

#### 2.2.2. Response Surface Modeling

_{1}), tooth bite (X

_{2}), and drill type (X

_{3}) on delamination factor at inlet (Y

_{1}), delamination factor at outlet (Y

_{2}), thrust force (Y

_{3}), and drilling torque (Y

_{4}), which are the dependent variables analyzed in this work. The values of analyzed input factors are presented in Table 2. Moreover, the RSM was used to find the optimum values of analyzed factors together with a Box–Wilson central composite design (CCD). This design contains:

- two-level factorial points (Figure 7), which analyze all combinations of the low (−1) and high (+1) levels of analyzed factors, namely eight combinations (four combinations for flat drill and four combinations for helical drill), namely, combinations #1, #6, #8, #13, #16, #23, #24, and #25 (Table 3);
- axial points (Figure 7 and Table 3), which are needed to estimate the non-linear effect of analyzed factors. In this work, the α was equal to 1, therefore a face centered design was applied. Eight combinations (four combination for each type of drill) were analyzed in this study, namely (combinations #3, #4, #10, #14, #17, #18, #19, and #22);

^{2}).

_{i}), into an individual desirability function (d

_{i}), which may have a value between 0 and 1. If the analyzed response fulfills the optimization goal, the d

_{i}= 1. All individual desirabilities are combined by means of geometric mean that describes the overall desirability, D (Equation (6)) [42]:

## 3. Results and Discussion

#### 3.1. ANN Modeling

^{2}) among 0.78 and 0.98. Therefore, it could be affirmed that the designed artificial neural network models could explain at least 78% in the model developed to predict the delamination factor at the outlet and at least 98% of the experimental values in the case of the model designed to forecast the drilling torque. The values of the performance indicator (R

^{2}) are in the range with data reporting in previous studies regarding the application of ANN modeling techniques in wood machining; namely, Özşahin and Singer [19] obtained a R

^{2}of 0.98 for a neural network trained to predict the noise emission during wood machining. Nasir and Cool [20] obtained a coefficient of determination between 0.67 and 0.99 for various network architectures that were designed to predict the dust emission during wood sawing. Gürgen et al. [24] attained a R

^{2}of 0.96 for an ANN model designed to predict the surface roughness. Tiryaki et al. [18] designed an ANN model that is able to predict the power consumption in wood planning with a R

^{2}of 0.97. Additionally, the neural network designed by Zbieć [16] to monitor the tool wear during milling of MDF earned a high coefficient of determination (R

^{2}= 0.99). In conclusion, the designed neural networks have a high predictability. How well the designed ANN models performed could be inspected, also from Figure 9, wherein one could observe that the predicted values are close to the experimental ones.

#### 3.2. Response Surface Methodology

#### 3.2.1. Delamination Factor at the Inlet

_{1}) in the case of the flat and helical drill.

_{3}) has a bigger influence than the drill tip angle (X

_{1}) and tooth bite (X

_{2}). This result is contrary to the results obtained in the case of prelaminated particleboards, where the most important factor that affects the delamination factor at inlet (Y

_{1}) is the tooth bite [14]. This result is correlated with data reported in the literature; namely, the feed rate and drill tip angle play an important role on the value of delamination factor [2,6,8,9,12]. In addition, in this study, it was found that there is an interaction between the independent variables. The most important interaction is between drill tip angle and drill type (X

_{1}X

_{3}) and between tooth bite and drill type (X

_{2}X

_{3}). Since there is a non-linear effect on the drill tip angle and tooth bite factor, the optimum values are inside the analyzed range (Table 1). The ANOVA results (α = 0.05) are presented in Table 7. In Figure 10, the influence of the drill tip angle (X

_{1}) and tooth bite (X

_{2}) on the delamination factor at the inlet during MDF drilling can be observed.

#### 3.2.2. Delamination Factor at the Outlet

_{2}) are presented by Equations (10)–(12). The models are significant at 1%. Based on Equation (9), one could observe that the most important factor that influences the delamination factor at outlet is the drill type (X

_{3}), which is similar with that obtained in the case of the delamination factor at inlet. The second factor is the drill tip angle (X

_{1}). The third one is the tooth bite (X

_{2}). Moreover, the results are similar with data reported in the literature; namely, a small tip angle with a low feed rate assures a lower delamination factor during drilling of MDF [2]. The most important interaction is between drill tip angle and tooth bite (X

_{1}X

_{2}). By comparing the results regarding the most important factor that affects the delamination factor at outlet during drilling of MDF boards, one could observe that the obtained result is the same as that obtained in the case of prelaminated wood particleboards [14]. The ANOVA results (α = 0.05) are presented in Table 8. In Figure 11 is presented the synergetic effects of the drill tip angle (X

_{1}) and tooth bite (X

_{2}) on the delamination factor at the outlet (Y

_{2}).

#### 3.2.3. Thrust Force

_{3}) are shown in Equations (13)–(15). The most important factor that influences the trust force during the drilling of MDF boards is the same as in the case of prelaminated wood particleboards, namely drill type [14]. The second one is the tooth bite and drill tip angle. The results are supported by the data in the literature, namely that the thrust force is affected by the feed rate [44,45]. The interaction between tooth bite and drill type has a bigger effect than the others, namely between tooth bite and drill tip angle or the interaction between drill tip angle and drill type. This interaction is pictured in Figure 11. The ANOVA results (α = 0.05) are presented in Table 9. In Figure 12 is presented the interaction effects of the drill tip angle (X

_{1}) and tooth bite (X

_{2}) on the thrust force (Y

_{3}).

#### 3.2.4. Drilling Torque

_{4}) than the other two analyzed factors. Drill tip angle affects more the drilling torque than the drill type. The obtained result is the same as that obtained in the case of prelaminated wood particleboards [14]. In addition, the findings are correlated with data from literature, namely that the drilling torque is influenced by the feed rate and tip angle during drilling of MDF [2].

_{1}X

_{2}> X

_{2}X

_{3}> X

_{1}X

_{3}). The ANOVA results are presented in Table 10. In Figure 13 is presented the influence of the drill tip angle and tooth bite on the drilling torque. Equations (17) and (18) could be used to predict the drilling torque (Y

_{4}) based on the drill tip angle (X

_{1}) and tooth bite (X

_{2}).

- The helical drill, together with a low tooth bite assure a high quality and low energy consumption both for MDF panels and prelaminated wood particleboards.
- Regarding the flat drill, the optimum value of drill tip angle (X
_{1}) is 30° or 60° for MDF boards, compared to prelaminated wood particleboards wherein the value was 30°, 60°, or 90°. Therefore, it could be concluded that for flat drills, a drill tip equal to 30° or 60° assures a high drilling quality and a lower energy consumption both in the case of MDF and prelaminated wood particleboards. - The relative errors between predicted and experimental values are lower than those that were obtained in the case of our previous work regarding the drilling of prelaminated wood particleboards. In this study, the error was between 0.09 and 3.9% in the case of the delamination factor; 1.7 and 13.5% in the case of the thrust force; and 0.2 and 0.5% for the drilling torque. Therefore, it could be concluded that the developed regression equations for MDF boards performs better than those designed for prelaminated wood particleboards.

^{a}—drill tip angle was considered equal to 60°;

^{b}—drill tip angle was considered equal to 90°.

_{R}is the relative error (%), Y is the experimental value and $\widehat{\mathrm{Y}}$ is the predicted value.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Kamperidou, V. Drilling of Wood and Wood-Based Panels. In Proceedings of the Tenth Scientific and Technical Conference “Innovations in Forest Industry and Engineering Design” INNO 2020, Sofia, Bulgaria, 1–3 October 2020; Available online: https://www.researchgate.net/publication/344695192_DRILLING_OF_WOOD_AND_WOOD-BASED_PANELS (accessed on 11 November 2023).
- Szwajka, K.; Trzepiecinski, T. On the machinability of medium density fiberboard by drilling. Bioresources
**2019**, 13, 8263–8278. [Google Scholar] [CrossRef] - Sydor, M.; Rogoziński, T.; Stuper-Szablewska, K.; Starczewski, K. The accuracy of holes drilled in the side surface of plywood. BioRes
**2020**, 15, 117–129. [Google Scholar] [CrossRef] - Kurek, J.; Krupa, A.; Antoniuk, I.; Akhmet, A.; Abdiomar, U.; Bukowski, M.; Szymanowski, K. Improved Drill State Recognition during Milling Process Using Artificial Intelligence. Sensors
**2023**, 23, 448. [Google Scholar] [CrossRef] [PubMed] - Ispas, M.; Răcășan, S. Study regarding the influence of the tool geometry and feed rate on the drilling quality of MDF panels. Pro Ligno
**2017**, 13, 174–180. [Google Scholar] - Davim, P.J.; Clemente, V.C.; Silva, S. Drilling investigation of MDF (medium density fibreboard). J. Mater. Process. Technol.
**2007**, 203, 537–541. [Google Scholar] [CrossRef] - Palanikumar, K.; Prakash, S.; Manoharan, N. Experimental Investigation and Analysis on Delamination in Drilling of Wood Composite Medium Density Fiber Boards. Mater. Manuf. Process.
**2009**, 24, 1341–1348. [Google Scholar] [CrossRef] - Prakash, S.; Palanikumar, K.; Manoharan, N. Optimization of delamination factor in drilling medium-density fiberboards (MDF) using desirability-based approach. Int. J. Adv. Manuf. Technol.
**2009**, 45, 370–381. [Google Scholar] [CrossRef] - Valarmathi, T.N.; Palanikumar, K.; Sekar, S. Parametric analysis on delamination in drilling of wood composite panels. Indian J. Sci. Technol.
**2013**, 6, 1–10. [Google Scholar] [CrossRef] - Gaitonde, V.N.; Karnik, S.R.; Davim, J.P. Taguchi multiple-performance characteristics optimization in drilling of medium density fibreboard (MDF) to minimize delamination using utility concept. J. Mater. Process. Technol.
**2008**, 196, 73–78. [Google Scholar] [CrossRef] - Ayyildiz, E.A.; Ayyildiz, M.; Kara, F. Optimization of Surface Roughness in Drilling Medium-Density Fiberboard with a Parallel Robot. Adv. Mater. Sci. Eng.
**2021**, 2021, 6658968. [Google Scholar] [CrossRef] - Prakash, S.; LillyMercy, J.; Manoj, K.S.; Vineeth, K.S.M. Optimization of drilling characteristics using Grey Relational Analysis (GRA) in Medium Density Fiber Board (MDF). Mater. Today Proc.
**2015**, 2, 1541–1551. [Google Scholar] - Prakash, S.; Palanikumar, K. Modeling for prediction of surface roughness in drilling MDF panels using response surface methodology. J. Compos. Mater.
**2010**, 45, 1639–1646. [Google Scholar] [CrossRef] - Bedelean, B.; Ispas, M.; Răcășan, S.; Baba, M.N. Optimization of Wood Particleboard Drilling Operating Parameters by Means of the Artificial Neural Network Modeling Technique and Response Surface Methodology. Forests
**2022**, 13, 1045. [Google Scholar] [CrossRef] - Szwajka, K.; Zielinska-Szwajka, J.; Gorski, J. Neural networks based in process tool wear prediction system in milling wood operations. In Proceedings of the Fifth International Symposium on Instrumentation Science and Technology, Shenyang, China, 12 January 2009. [Google Scholar] [CrossRef]
- Zbieć, M. Application of neural network in simple tool wear monitoring and identification system in MDF milling. Drv. Ind.
**2011**, 62, 43–54. [Google Scholar] [CrossRef] - Tiryaki, S.; Özşahin, Ş.; Aydin, A. Employing artificial neural networks for minimizing surface roughness and power consumption in abrasive machining of wood. Eur. J. Wood Prod.
**2017**, 75, 347–358. [Google Scholar] [CrossRef] - Tiryaki, S.; Malkoçoğlu, A.; Özşahin, Ş. Artificial neural network modeling to predict optimum power consumption in wood machining. Drewno
**2016**, 59, 109–125. [Google Scholar] [CrossRef] - Özşahin, S.; Singer, H. Prediction of noise emission in the machining of wood materials by means of an artificial neural network. N. Z. J. For. Sci.
**2022**, 52, 1–10. [Google Scholar] [CrossRef] - Nasir, V.; Cool, J. Characterization, optimization, and acoustic emission monitoring of airborne dust emission during wood sawing. Int. J. Adv. Manuf. Technol.
**2020**, 109, 2365–2375. [Google Scholar] [CrossRef] - Rabiei, F.; Yaghoubi, S. A comprehensive investigation on the influences of optimal CNC wood machining variables on surface quality and process time using GMDH neural network and bees optimization algorithm. Mater. Today Commun.
**2023**, 36, 106482. [Google Scholar] [CrossRef] - Demir, A.; Osman, E.C.; Aydin, I. Determination of CNC processing parameters for the best wood surface quality via artificial neural network. Wood Mater. Sci. Eng.
**2022**, 17, 685–692. [Google Scholar] [CrossRef] - Cakmak, A.; Malkocoglu, A.; Ozsahin, S. Optimization of wood machining parameters using artificial neural network in CNC router. Mater. Sci. Technol.
**2023**, 39, 1728–1744. [Google Scholar] [CrossRef] - Gürgen, A.; Çakmak, A.; Yildiz, S.; Malkoçoğlu, A. Optimization of CNC operating parameters to minimize surface roughness of Pinus sylvestris using integrated artificial neural network and genetic algorithm. Maderas. Cienc. Tecnol.
**2022**, 24, 1–12. [Google Scholar] [CrossRef] - Sofuoglu, S.D. Using artificial neural networks to model the surface roughness of massive wooden edge-glued panels made of Scotch pine (Pinus sylvestris L.) in a machining process with computer numerical control. BioRes
**2015**, 10, 6797–6808. [Google Scholar] [CrossRef] - Nasir, V.; Cool, J.; Sassani, F. Acoustic emission monitoring of sawing process: Artificial intelligence approach for optimal sensory feature selection. Int. J. Adv. Manuf. Technol.
**2019**, 102, 4179–4197. [Google Scholar] [CrossRef] - Nasir, V.; Cool, J. Intelligent wood machining monitoring using vibration signals combined with self-organizing maps for automatic feature selection. Int. J. Adv. Manuf. Technol.
**2020**, 108, 1811–1825. [Google Scholar] [CrossRef] - Nasir, V.; Dibaji, S.; Alaswad, K.; Cool, J. Tool wear monitoring by ensemble learning and sensor fusion using power, sound, vibration, and AE signals. Manuf. Lett.
**2021**, 30, 32–38. [Google Scholar] [CrossRef] - Nasir, V.; Kooshkbaghi, M.; Cool, J.; Sassani, F. Cutting tool temperature monitoring in circular sawing: Measurement and multi-sensor feature fusion-based prediction. Int. J. Adv. Manuf. Technol.
**2021**, 112, 2413–2424. [Google Scholar] [CrossRef] - Stanojevic, D.; Mandic, M.; Danon, G.; Svrzic, S. Prediction of the surface roughness of wood for machining. J. For. Res.
**2017**, 28, 1281–1283. [Google Scholar] [CrossRef] - Ahmed, M.; Kamal, K.; Ratlamwala, T.A.H.; Hussain, G.; Alqahtani, M.; Alkahtani, M.; Alatefi, M.; Alzabidi, A. Tool Health Monitoring of a Milling Process Using Acoustic Emissions and a ResNet Deep Learning Model. Sensors
**2023**, 23, 3084. [Google Scholar] [CrossRef] - Jegorowa, A.; Górski, J.; Kurek, J.; Kruk, M. Initial study on the use of support vector machine (SVM) in tool condition monitoring in chipboard drilling. Eur. J. Wood Prod.
**2019**, 77, 957–959. [Google Scholar] [CrossRef] - Nasir, V.; Cool, J. A review on wood machining: Characterization, optimization, and monitoring of the sawing process. Wood Mater. Sci. Eng.
**2020**, 15, 1–16. [Google Scholar] [CrossRef] - Nasir, V.; Sassani, F. A review on deep learning in machining and tool monitoring: Methods, opportunities, and challenges. Int. J. Adv. Manuf. Technol.
**2021**, 115, 2683–2709. [Google Scholar] [CrossRef] - Budău, G.; Ispas, M. Woodworking Machine-Tools; Lux Libris Publishing House: Brasov, Romania, 2014. (In Romanian) [Google Scholar]
- Watanabe, K.; Korai, H.; Matsushita, Y.; Hayashi, T. Predicting internal bond strength of particleboard under outdoor exposure based on climate data: Comparison of multiple linear regression and artificial neural network. J. Wood Sci.
**2015**, 61, 151–158. [Google Scholar] [CrossRef] - Fahlman, S.E.; Lebiere, C. The Cascade-Correlation Learning Architecture; Technical Report CMU-CS-90-100; School of Computer Science, Carnegie Mellon University: Pittsburgh, PA, USA, 1990. [Google Scholar]
- Avramidis, S.; Iliadis, L. Predicting wood thermal conductivity using artificial neural networks. Wood Fiber Sci.
**2005**, 37, 682–690. [Google Scholar] - Monticeli, F.M.; Neves, R.M.; Ornaghi, H.L.; Almeida, J.H.S. Prediction of Bending Properties for 3D-Printed Carbon Fibre/Epoxy Composites with Several Processing Parameters Using ANN and Statistical Methods. Polymers
**2022**, 14, 3668. [Google Scholar] [CrossRef] - Dubdub, I. Artificial Neural Network Study on the Pyrolysis of Polypropylene with a Sensitivity Analysis. Polymers
**2023**, 15, 494. [Google Scholar] [CrossRef] - Myers, R.H.; Montgomery, D.C.; Anderson-Cook, C.M. Response Surface Methodology: Process and Product Optimization Using Designed Experiments; Wiley Series in Probability and Statistics; Wiley: Hoboken, NJ, USA, 2016; pp. 6–262. [Google Scholar]
- NIST/SEMATECH. e-Handbook of Statistical Methods. Available online: http://www.itl.nist.gov/div898/handbook/ (accessed on 18 October 2023).
- Podziewski, P.; Szymanowski, K.; Górski, J.; Czarniak, P. Relative machinability of wood-based boards in the case of drilling Experimental study. BioResources
**2018**, 13, 1761–1772. [Google Scholar] [CrossRef] - Valarmathi, T.N.; Palanikumar, K.; Sekar, S. Modeling of thrust force in drilling of plain medium density fiberboard (MDF) composite panels using RSM. Procedia Eng.
**2012**, 38, 1828–1835. [Google Scholar] [CrossRef] - Kumar, K.; Davim, J.P. Biodegradable Composites: Materials, Manufacturing and Engineering; De Gruyter: Berlin, Germany; Boston, MA, USA, 2019; pp. 167–182. [Google Scholar] [CrossRef]

**Figure 2.**MDF samples used for drilling experiments: (

**a**) shape and dimensions; (

**b**) processed sample; and (

**c**) the approach used to measure the diameters in order to calculate the delamination factor.

**Figure 3.**The machine tool and the measuring device: (

**a**) ISEL GFV/GFY CNC processing centre; (

**b**) the forces measuring device.

**Figure 7.**The representation of a face central composite design and the analyzed combinations among factors (−1 is the low level of factor; +1 is the high level of factor; 0—is the middle value of factor; and ±α is the axial or star points).

**Figure 8.**The architecture of ANN models, which were designed to predict the delamination factor at the inlet (Y

_{1}); delamination factor at the outlet (Y

_{2}); thrust force (Y

_{3}); and drilling torque (Y

_{4}).

**Figure 9.**A comparison between the predicted and experimental responses: (

**a**) delamination factor at the inlet; (

**b**) delamination factor at the outlet; (

**c**) thrust force; and (

**d**) drilling torque.

**Figure 10.**The influence of the drill tip angle and tooth bite on the delamination factor at the inlet: flat drill (

**a**) and helical drill (

**b**).

**Figure 11.**The influence of the drill tip angle and tooth bite on the delamination factor at the outlet: flat drill (

**a**) and helical drill (

**b**).

**Figure 12.**The influence of the drill tip angle and tooth bite on the thrust force: flat drill (

**a**) and helical drill (

**b**).

**Figure 13.**The influence of the drill tip angle and tooth bite on the drilling torque: flat drill (

**a**) and helical drill (

**b**).

Independent Variable | Analyzed Values | |||
---|---|---|---|---|

Drill point angle (X_{1}), ° | 30 | 60 | 90 | 120 |

Tooth bite (X_{2}), mm | 0.1 | 0.3 | 0.5 | 0.7 |

Drill type (X_{3}) | Flat | Helical |

Numeric Factor | Level | ||||
---|---|---|---|---|---|

−α * | −1 | 0 | +1 | +α * | |

Drill tip angle (X_{1}), ° | 30 | 30 | 75 | 120 | 120 |

Tooth bite (X_{2}), mm | 0.1 | 0.1 | 0.4 | 0.7 | 0.7 |

Categoric Factor | Level 1 | Level 2 | |||

Drill type (X_{3}) | Flat (−1) | Helical (+1) |

Combination # | Independent Variables (Factors) | Dependent Variables (Responses) | |||||
---|---|---|---|---|---|---|---|

Drill Tip Angle (X_{1}), ° | Tooth Bite (X_{2}), mm | Drill Type (X_{3}) | Y_{1} | Y_{2} | Y_{3} | Y_{4} | |

1 | 30 (−1) | 0.1 (−1) | Flat (−1) | 1.07 | 1.13 | 115.34 | 0.55 |

2 | 75 (0) | 0.4 (0) | Flat (−1) | 1.10 | 1.25 | 252.07 | 0.89 |

3 | 120 (+α) | 0.4 (0) | Flat (−1) | 1.11 | 1.44 | 272.69 | 0.60 |

4 | 120 (+α) | 0.4 (0) | Helical (1) | 1.00 | 1.03 | 68.53 | 0.33 |

5 | 75 (0) | 0.4 (0) | Helical (1) | 1.00 | 1.00 | 76.85 | 0.53 |

6 | 120 (1) | 0.7 (1) | Helical (1) | 1.18 | 1.03 | 102.67 | 0.41 |

7 | 75 (0) | 0.4 (0) | Helical (1) | 1.00 | 1.00 | 76.85 | 0.53 |

8 | 120 (1) | 0.1 (−1) | Helical (1) | 1.00 | 1.03 | 64.23 | 0.16 |

9 | 75 (0) | 0.4 (0) | Helical (1) | 1.00 | 1.00 | 76.85 | 0.53 |

10 | 75 (0) | 0.7 (+α) | Flat (−1) | 1.12 | 1.25 | 366.90 | 1.52 |

11 | 75 (0) | 0.4 (0) | Flat (−1) | 1.10 | 1.25 | 252.07 | 0.89 |

12 | 75 (0) | 0.4 (0) | Helical (1) | 1.00 | 1.00 | 76.85 | 0.53 |

13 | 30 (−1) | 0.7 (1) | Helical (1) | 1.10 | 1.00 | 49.87 | 1.17 |

14 | 75 (0) | 0.1 (−α) | Helical (1) | 1.00 | 1.00 | 72.19 | 0.24 |

15 | 75 (0) | 0.4 (0) | Flat (−1) | 1.10 | 1.25 | 252.07 | 0.89 |

16 | 30 (−1) | 0.7 (1) | Flat (−1) | 1.06 | 1.13 | 372.29 | 1.74 |

17 | 75 (0) | 0.1 (−α) | Flat (−1) | 1.08 | 1.25 | 138.16 | 0.36 |

18 | 30 (−α) | 0.4 (0) | Flat (−1) | 1.09 | 1.13 | 305.67 | 1.28 |

19 | 75 (0) | 0.7 (+α) | Helical (1) | 1.00 | 1.00 | 75.38 | 0.73 |

20 | 75 (0) | 0.4 (0) | Flat (−1) | 1.10 | 1.25 | 252.07 | 0.89 |

21 | 75 (0) | 0.4 (0) | Flat (−1) | 1.10 | 1.25 | 252.07 | 0.89 |

22 | 30 (−α) | 0.4 (0) | Helical (1) | 1.00 | 1.00 | 33.46 | 0.77 |

23 | 120 (1) | 0.1 (−1) | Flat (−1) | 1.08 | 1.44 | 137.27 | 0.23 |

24 | 120 (1) | 0.7 (1) | Flat (−1) | 1.13 | 1.44 | 334.78 | 0.74 |

25 | 30 (−1) | 0.1 (−1) | Helical (1) | 1.00 | 1.00 | 28.89 | 0.35 |

26 | 75 (0) | 0.4 (0) | Helical (1) | 1.00 | 1.00 | 76.85 | 0.53 |

Independent Variables | Goal Settings | Minimum Value | Maximum Value | Level of Factor Importance |
---|---|---|---|---|

Drill tip angle (X_{1}) | In range | 30 | 120 | 3 |

Tooth bite (X_{2}) | 0.1 | 0.7 | 3 | |

Drill type (X_{3}) | Flat | Helical | 3 | |

Dependent Variables | ||||

Delamination factor at the inlet (Y_{1}) | Minimize | 1 | 1.18 | 3 |

Delamination factor at the outlet (Y_{2}) | 1 | 1.43 | 3 | |

Thrust force (Y_{3}) | 28.88 | 372.28 | 3 | |

Drilling torque (Y_{4}) | 0.15 | 1.73 | 3 |

Model Output | Number of Neurons in the Layers of ANN Models | Coefficient of Correlation (R) | Coefficient of Determination (R^{2}) | ||||||
---|---|---|---|---|---|---|---|---|---|

Input | Hidden | Outlet | Training | Testing | Validation | Training | Testing | Validation | |

Delamination factor at the inlet | 3 | 6 | 1 | 0.86 | 0.89 | 0.92 | 0.73 | 0.79 | 0.85 |

Delamination factor at the outlet | 3 | 9 | 1 | 0.85 | 0.88 | 0.88 | 0.72 | 0.77 | 0.78 |

Thrust force | 3 | 10 | 1 | 0.99 | 0.98 | 0.99 | 0.98 | 0.96 | 0.98 |

Drilling torque | 3 | 11 | 1 | 0.98 | 0.98 | 0.98 | 0.96 | 0.96 | 0.97 |

**Table 6.**The performance criteria of selected ANN topology in the case of particle boards (PB) drilling [14].

Model Output | Number of Neurons in the Layers of ANN Models | Coefficient of Correlation (R) | Coefficient of Determination (R^{2}) | ||||||
---|---|---|---|---|---|---|---|---|---|

Input | Hidden | Outlet | Training | Testing | Validation | Training | Testing | Validation | |

Delamination factor at the inlet | 3 | 13 | 1 | 0.76 | 0.72 | 0.67 | 0.57 | 0.51 | 0.44 |

Delamination factor at the outlet | 3 | 6 | 1 | 0.88 | 0.88 | 0.90 | 0.77 | 0.77 | 0.82 |

Thrust force | 3 | 4 | 1 | 0.94 | 0.95 | 0.96 | 0.88 | 0.90 | 0.92 |

Drilling torque | 3 | 9 | 1 | 0.97 | 0.97 | 0.98 | 0.94 | 0.94 | 0.97 |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value Prob > F | Observation |
---|---|---|---|---|---|---|

Model | 0.067 | 11 | 0.006114 | 7.68 | 0.0003 | Significant |

Drill tip angle (X_{1}) | 0.0268 | 1 | 0.002683 | 3.37 | 0.087 | Not significant |

Tooth bite (X_{2}) | 0.011 | 1 | 0.011 | 13.68 | 0.0024 | Significant |

Drill type (X_{3}) | 0.038 | 1 | 0.038 | 47.87 | <0.0001 | Significant |

X_{1}X_{2} | 0.00259 | 1 | 0.00259 | 3.25 | 0.0928 | Not significant |

X_{1}X_{3} | 0.0000312 | 1 | 0.0000312 | 0.039 | 0.8457 | Not significant |

X_{2}X_{3} | 0.003789 | 1 | 0.003789 | 4.76 | 0.0467 | Significant |

X_{1}^{2} | 0.0009446 | 1 | 0.0009446 | 1.19 | 0.2943 | Not significant |

X_{2}^{2} | 0.00079 | 1 | 0.0007909 | 0.99 | 0.3357 | Not significant |

X_{1}X_{2}X_{3} | 0.00002274 | 1 | 0.00002274 | 0.029 | 0.8682 | Not significant |

X_{1}^{2}X_{3} | 0.002513 | 1 | 0.002513 | 3.16 | 0.0973 | Not significant |

X_{2}^{2} X_{3} | 0.002725 | 1 | 0.002725 | 3.42 | 0.0854 | Not significant |

R^{2} | 0.85 |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value Prob > F | Observation |
---|---|---|---|---|---|---|

Model | 0.59 | 8 | 0.073 | 2409.57 | <0.0001 | Significant |

Drill tip angle (X_{1}) | 0.084 | 1 | 0.084 | 2757.18 | <0.0001 | Significant |

Tooth bite (X_{2}) | 0 | 1 | 0 | 0 | 1 | Not significant |

Drill type (X_{3}) | 0.44 | 1 | 0.44 | 14587.86 | <0.0001 | Significant |

X_{1}X_{2} | 0 | 1 | 0 | 0 | 1 | Not significant |

X_{1}X_{3} | 0.055 | 1 | 0.055 | 1826.64 | <0.0001 | Significant |

X_{2}X_{3} | 0 | 1 | 0 | 0 | 1 | Not significant |

X_{1}^{2} | 0.0027 | 1 | 0.0027 | 89.64 | <0.0001 | Significant |

X_{2}^{2} | 0 | 1 | 0 | 0 | 1 | Not significant |

R^{2} | 0.99 |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value Prob > F | Observation |
---|---|---|---|---|---|---|

Model | 311,000 | 11 | 28271 | 171.78 | <0.0001 | Significant |

Drill tip angle (X_{1}) | 464.278 | 1 | 464.28 | 2.82 | 0.1152 | Not significant |

Tooth bite (X_{2}) | 46,351.60 | 1 | 46,351.61 | 281.66 | <0.0001 | Significant |

Drill type (X_{3}) | 98,114.63 | 1 | 98,114.63 | 596.19 | <0.0001 | Significant |

X_{1}X_{2} | 220.32 | 1 | 220.32 | 1.34 | 0.2666 | Not significant |

X_{1}X_{3} | 2458.85 | 1 | 2458.85 | 14.94 | 0.0017 | Significant |

X_{2}X_{3} | 32,092.03 | 1 | 32,092.03 | 195.007 | <0.0001 | Significant |

X_{1}^{2} | 53.67 | 1 | 53.67 | 0.326 | 0.5777 | Not significant |

X_{2}^{2} | 557.86 | 1 | 557.86 | 3.39 | 0.086 | Not significant |

X_{1}X_{2}X_{3} | 739.12 | 1 | 739.12 | 4.49 | 0.0524 | Not significant |

X_{1}^{2}X_{3} | 1454.28 | 1 | 1454.28 | 8.84 | 0.0101 | Significant |

X_{2}^{2}X_{3} | 1005.80 | 1 | 1005.80 | 6.11 | 0.0269 | Significant |

R^{2} | 0.99 |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value Prob > F | Observation |
---|---|---|---|---|---|---|

Model | 3.786 | 6 | 0.63 | 166.44 | <0.0001 | Significant |

Drill tip angle (X_{1}) | 0.957 | 1 | 0.957 | 252.48 | <0.0001 | Significant |

Tooth bite (X_{2}) | 1.625 | 1 | 1.625 | 428.79 | <0.0001 | Significant |

Drill type (X_{3}) | 0.835 | 1 | 0.835 | 220.36 | <0.0001 | Significant |

X_{1}X_{2} | 0.19 | 1 | 0.19 | 51.35 | <0.0001 | Significant |

X_{1}X_{3} | 0.032 | 1 | 0.032 | 8.46 | 0.0090 | Significant |

X_{2}X_{3} | 0.14 | 1 | 0.14 | 37.24 | <0.0001 | Significant |

R^{2} | 0.98 |

Solution No. | X_{1} | X_{2} | X_{3} | Delamination Factor at the Inlet | Delamination Factor at the Outlet | Trust Force (N) | Drilling Torque (Nm) | D | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\widehat{{\mathbf{Y}}_{1}}$ | Y_{1} | E_{R1} | $\widehat{{\mathbf{Y}}_{2}}$ | Y_{2} | E_{R2} | $\widehat{{\mathbf{Y}}_{3}}$ | Y_{3} | E_{R3} | $\widehat{{\mathbf{Y}}_{4}}$ | Y_{4} | E_{R4} | |||||

1 | 64 | 0.1 | Helical | 0.980 | 1 ^{a} | 2.00 | 0.995 | 1 ^{a} | 0.50 | 63.14 | 62.09 ^{a} | −1.7 | 0.281 | 0.33 ^{a} | 0.33 | 0.95 |

2 | 89 | 0.1 | Helical | 0.979 | 1 ^{b} | 2.10 | 1.004 | 1 ^{b} | −0.40 | 71.14 | 62.7 ^{b} | −13.5 | 0.240 | 0.21 ^{b} | 0.21 | 0.95 |

3 | 30 | 0.1 | Flat | 1.07 | 1.03 | −3.88 | 1.129 | 1.13 | 0.09 | 127.86 | 121.23 | −5.5 | 0.583 | 0.51 | 0.51 | 0.680 |

4 | 58 | 0.1 | Flat | 1.08 | 1.06 ^{a} | −1.89 | 1.20 | 1.16 ^{a} | −3.45 | 120.80 | 127.62 ^{a} | 5.4 | 0.470 | 0.44 ^{a} | 0.44 | 0.643 |

^{a}—drill tip angle was considered equal to 60°;

^{b}—drill tip angle was considered equal to 90°.

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## Share and Cite

**MDPI and ACS Style**

Bedelean, B.; Ispas, M.; Răcășan, S.
Combining Artificial Neural Network and Response Surface Methodology to Optimize the Drilling Operating Parameters of MDF Panels. *Forests* **2023**, *14*, 2254.
https://doi.org/10.3390/f14112254

**AMA Style**

Bedelean B, Ispas M, Răcășan S.
Combining Artificial Neural Network and Response Surface Methodology to Optimize the Drilling Operating Parameters of MDF Panels. *Forests*. 2023; 14(11):2254.
https://doi.org/10.3390/f14112254

**Chicago/Turabian Style**

Bedelean, Bogdan, Mihai Ispas, and Sergiu Răcășan.
2023. "Combining Artificial Neural Network and Response Surface Methodology to Optimize the Drilling Operating Parameters of MDF Panels" *Forests* 14, no. 11: 2254.
https://doi.org/10.3390/f14112254