# Evaluation of Prediction Models of the Microwire EDM Process of Inconel 718 Using ANN and RSM Methods

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Workpiece Material

#### 2.2. Experimental Setup

- U—average discharge voltage,
- I—the height of the peak current during discharging,
- t
_{on}—pulse time.

_{off}, and the wire speed WS on the parameters describing properties of the surface topography and the material removal rate of Inconel 718 after micro-WEDM were conducted using Hartley’s experimental design with three five-level parameters. Table 3 shows the levels of the machining parameters used in the experiment. Using five-level DOE allows for investigation in a wide range (five levels) influence input parameters on the investigated output. For example, in the preliminary research, the range of parameters for micro-WEDM of Inconel 718 was established for criteria: stable discharges (observed current and voltage waveforms) without the wire breaking.

## 3. Results and Discussion

#### 3.1. Analysis of the Surface Topography

^{2}/min.

#### 3.2. Predictive Models

_{off}), and the wire speed (WS); the output parameters were the surface roughness (Sa), the roughness of the core (Sk), the roughness of the peak (Spk), the roughness of the valleys (Svk), and the MRR.

#### 3.2.1. Response Surface Methodology

_{off},WS) ± ε,

_{off}(time interval), and WS (wire speed) are independent parameters; and ε is the experimental error.

^{2}and the Fisher test, it was found that the best match to the results of the experimental research was obtained for the second-degree polynomial function. In the next step, analysis of variance (ANOVA) was used to develop the final regression equation. At the 95% coefficient level, the significance of each factor in the regression model was checked. If the calculated probability value Prob > f for the single factor was higher than 0.05, this meant that the factor was nonsignificant and was removed from the final regression function. The ANOVA results for surface roughness (Sa), the roughness of the core (Sk), the roughness of the peak (Spk), the roughness of the valleys (Svk), and the MRR are presented in Table 5, Table 6, Table 7, Table 8 and Table 9, respectively and are included in the Supplementary Materials.

^{2}and the adjusted coefficient of determination (R-Adj) for the Sa, Svk, and the MRR models were over 92% and 90%, respectively, and those for Spk and Sk were over 84% and 81%, respectively. The response function developed here had a very good fit with the experimental results.

^{2}− 0.2832 t

_{off}+ 0.0155 t

_{off}

^{2}(μm)

^{2}− 0.0020 WS t

_{off}(μm)

^{2}+0.7470 WS − 0.0450 WS

^{2}− 0.33859 t

_{off}+ 0.0183 t

_{off}

^{2}(μm)

_{off}+ 0.0208 t

_{off}

^{2}0.06954 E WS (μm)

^{2}− 0.0232 WS

^{2}− 40.3947 t

_{off}+ 2.2594 t

_{off}

^{2}− 8.0758 E t

_{off}(mm

^{2}/min)

#### 3.2.2. Artificial Neural Network

_{off})) to the prediction model. The sensitivity analysis was the result of the quotient of the error calculated for the investigated ANN model network without one variable and the error calculated for the model with all variables. The sensitivity analysis results presented in Table 11 indicate that the factor with the greatest influence on the parameters describing the surface topography (Sa, Spk, Sk, and Svk) was the discharge energy, followed by the wire speed and the time interval. However, in the case of the material removal rate, the factor with the greatest influence was the time interval, then the discharge energy, followed by the wire speed.

#### 3.3. Evalutaion of the Predcitve Models

## 4. Conclusions

- Discharge energy made the main contribution to the surface roughness (Sa, Spk, Sv, and Svk) and the MRR during micro-WEDM of Inconel 718.
- The time interval made the main contribution to the MRR, as the decrease in the time interval increased the frequency of the discharge. Furthermore, for the adopted range, the time interval had the least influence on the parameters describing the surface topography’s properties.
- Wire-speed had the least influence on the parameters describing the surface topography’s properties (Sa, Spk, Sv, and Svk) and MRR. Furthermore, for the lowest wire speed, it was possible to obtain a high MRR and a low value of surface roughness. A decrease in the wire speed led to a decrease in the consumption of the electrode, which would have a significant impact on the environment and sustainability.
- The predictive models based on RSM and ANN for the micro-WEDM of Inconel 718 can be applied to construct technological tables for the investigated process.
- The models developed with ANN had a lower value for the relative error compared with the RSM models. The maximum relative error for the ANN models did not exceed 4%.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic illustration of the measuring circuit with the registered current and voltage waveforms.

**Figure 4.**Surface topography of Inconel 718 after micro-WEDM with the parameters E = 1.46 mJ, WS = 9 m/min, and t

_{off}= 8 µs: (

**a**) 3D texture; (

**b**) 2D profile of measured surface; (

**c**) SEM image.

**Figure 5.**EDS spectrum of the surface of Inconel 718 after micro-WEDM: E = 1.46 mJ, WS = 9 m/min, and t

_{off}= 8 µs.

**Figure 6.**Abbott-Firestone curves after micro-WEDM of Inconel 718: (

**a**) E = 0.21 mJ, WS = 9 m/min, and t

_{off}= 8 µs; (

**b**) E = 1.46 mJ, WS = 9 m/min, and t

_{off}= 8 µs.

**Figure 7.**Plots for the model of Sa: (

**a**) normal plot of the residuals, (

**b**) the residuals versus the predicted values, and (

**c**) the residuals versus the case number.

**Figure 13.**Estimated response plots for the RSM model of roughness (Sa): (

**a**) constant t

_{off}= 8 µs, (

**b**) constant WS = 9 m/min, and (

**c**) constant E = 0.7 mJ.

**Figure 14.**Estimated response plots for the ANN model of roughness (Sa): (

**a**) constant t

_{off}= 8 µs, (

**b**) constant WS = 9 m/min, and (

**c**) constant E = 0.7 mJ.

**Figure 15.**Estimated response plots for the RSM model of MRR: (

**a**) constant t

_{off}= 8 µs, (

**b**) constant WS = 9 m/min, and (

**c**) constant E = 0.7 mJ.

**Figure 16.**Estimated response plots for the ANN model of MRR: (

**a**) constant t

_{off}= 8 µs, (

**b**) constant WS = 9 m/min, and (

**c**) constant E = 0.7 mJ.

Ni | Cr | Nb | Mo | Ti | Al | Co | C | Mn | Si | P | S | B | Fe |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

50–55 | 17–21 | 4.75–5.5 | 2.8–3.3 | 0.65–1.15 | 0.2–0.8 | <1.0 | <0.015 | <0.5 | <0.35 | <0.015 | <0.015 | <0.06 | Balance |

Electrode | Brass wire, diameter 0.1 mm |

Workpiece material | Inconel 718 |

Height of specimen | 5 mm |

Discharge energy | 0.21–1.46 mJ |

Time interval t_{off} | 5–11 μs |

Open voltage U_{0} | 220 V |

Dielectric | Deionized water |

Wire mechanical tension | 0.2 daN |

Level | Parameter | ||
---|---|---|---|

Discharge Energy E (mJ) | Wire Speed (m/min) | Time Interval t _{off} (µm) | |

−1.68 | 0.21 | 6 | 5 |

−1 | 0.42 | 7 | 6 |

0 | 0.70 | 9 | 8 |

1 | 1.04 | 11 | 10 |

1.68 | 1.46 | 12 | 11 |

Exp. No. | WEDM Input | Observed Values | ||||||
---|---|---|---|---|---|---|---|---|

Discharge Energy E (mJ) | Wire Speed WS (m/min) | Time Interval t _{off} (μs) | Sa (μm) | Spk (μm) | Sk (μm) | Svk (μm) | MRR (mm ^{2}/min) | |

1. | 0.42 | 7 | 7 | 2.169 | 3.11 | 6.987 | 1.984 | 45.74 |

2. | 0.42 | 7 | 10 | 2.172 | 2.967 | 6.792 | 1.923 | 34.4 |

3. | 0.426 | 11 | 6 | 2.282 | 3.085 | 6.645 | 1.94 | 55.12 |

4. | 0.42 | 11 | 10 | 2.188 | 3.183 | 6.806 | 1.796 | 32.56 |

5. | 1.05 | 7 | 6 | 2.46 | 3.619 | 7.717 | 2.296 | 100.7 |

6. | 1.05 | 7 | 10 | 2.41 | 3.271 | 7.793 | 2.181 | 58.18 |

7. | 1.05 | 11 | 6 | 2.467 | 3.599 | 7.852 | 2.257 | 97.02 |

8. | 1.05 | 11 | 10 | 2.428 | 3.804 | 7.616 | 2.271 | 56.72 |

9. | 0.21 | 9 | 8 | 2.103 | 3.178 | 6.594 | 1.719 | 27.88 |

10. | 1.46 | 9 | 8 | 2.673 | 4.116 | 8.435 | 2.508 | 91.62 |

11. | 0.74 | 6 | 8 | 2.305 | 3.223 | 7.589 | 2.129 | 58.64 |

12. | 0.74 | 12 | 8 | 2.203 | 3.28 | 6.967 | 2.012 | 55.42 |

13. | 0.74 | 9 | 5 | 2.642 | 3.853 | 8.401 | 2.364 | 101.94 |

14. | 0.74 | 9 | 11 | 2.299 | 3.511 | 7.277 | 2.058 | 31.2 |

15. | 0.74 | 9 | 8 | 2.381 | 3.64 | 7.648 | 2.021 | 44.1 |

16. | 0.74 | 9 | 8 | 2.332 | 3.473 | 7.498 | 1.938 | 43.81 |

17. | 0.74 | 9 | 8 | 2.346 | 3.574 | 7.541 | 1.982 | 43.2 |

18. | 0.74 | 9 | 8 | 2.318 | 3.574 | 7.567 | 1.968 | 44.31 |

Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Value | Prob > f | Contribution % |
---|---|---|---|---|---|---|

Model | 0.3506 | 4 | 0.0876 | 39.96 | ||

E | 0.2599 | 1 | 0.2599 | 355.59 | 0.0003 | 74.14 |

WS^{2} | 0.0174 | 1 | 0.0174 | 23.93 | 0.0163 | 4.99 |

t_{off} | 0.0493 | 1 | 0.0493 | 67.54 | 0.0037 | 14.08 |

t_{off}^{2} | 0.0237 | 1 | 0.0237 | 32.52 | 0.0106 | 6.78 |

Error | 0.0021 | 13 | ||||

Total SS | 0.3527 | 17 | R-sqr = 0.92 | R-Adj = 0.90 |

Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Value | Prob > f | Contribution % |
---|---|---|---|---|---|---|

Model | 1.2631 | 3 | 0.4210 | 16.31 | ||

E | 0.8963 | 1 | 0.8963 | 48.73 | <0.0001 | 70.96 |

WS^{2} | 0.2717 | 1 | 0.2717 | 14.77 | 0.0017 | 21.51 |

t_{off} | 0.0950 | 1 | 0.0950 | 5.16 | 0.0392 | 7.53 |

Error | 0.0142 | 14 | ||||

Total SS | 1.5206 | 17 | R-sqr = 0.84 | R-Adj = 0.81 |

Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Value | Prob > f | Contribution % |
---|---|---|---|---|---|---|

Model | 4.1954 | 6 | 0.6992 | 58.51 | ||

E | 3.2785 | 1 | 3.2785 | 823.14 | <0.0001 | 78.15 |

E^{2} | 0.0988 | 1 | 0.0988 | 24.80 | 0.0155 | 2.36 |

WS | 0.1761 | 1 | 0.1761 | 44.21 | 0.0069 | 4.20 |

WS^{2} | 0.2511 | 1 | 0.2511 | 63.04 | 0.0041 | 5.99 |

t_{off} | 0.3491 | 1 | 0.3491 | 87.65 | 0.0025 | 8.32 |

t_{off}^{2} | 0.0416 | 1 | 0.0416 | 10.44 | 0.0481 | 0.99 |

Error | 0.0119 | 11 | ||||

Total SS | 4.2073 | 17 | R-sqr = 0.87 | R-Adj = 0.85 |

Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Value | Prob > f | Contribution % |
---|---|---|---|---|---|---|

Model | 0.6621 | 5 | 0.1317 | 36.96 | ||

E | 0.5196 | 1 | 0.5196 | 437.61 | 0.0002 | 78.92 |

WS | 0.0120 | 1 | 0.0120 | 10.15 | 0.0498 | 1.83 |

t_{off} | 0.0545 | 1 | 0.0545 | 45.90 | 0.0065 | 8.28 |

t_{off}^{2} | 0.0601 | 1 | 0.0601 | 50.66 | 0.0057 | 9.14 |

E WS | 0.0120 | 1 | 0.0120 | 10.16 | 0.0497 | 1.83 |

Error | 0.0035 | 12 | ||||

Total SS | 0.6585 | 17 | R-sqr = 0.95 | R-Adj = 0.92 |

Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Value | Prob > f | Contribution % |
---|---|---|---|---|---|---|

Model | 9016.25 | 6 | 1502.70 | 10.52 | ||

E | 3285.90 | 1 | 3285.90 | 253.14 | <0.0001 | 36.44 |

E^{2} | 175.54 | 1 | 175.54 | 13.52 | 0.0036 | 1.95 |

WS^{2} | 318.09 | 1 | 318.09 | 24.50 | 0.0004 | 3.53 |

t_{off} | 4234.76 | 1 | 4234.76 | 326.24 | <0.0001 | 46.97 |

t_{off}^{2} | 867.89 | 1 | 867.89 | 66.86 | <0.0001 | 9.63 |

E WS | 134.07 | 1 | 134.07 | 10.32 | 0.0082 | 1.49 |

Error | 142.78 | 11 | ||||

Total SS | 9159.03 | 17 | R-sqr = 0.98 | R-Adj = 0.98 |

Model | Number of Neurons in the Hidden Layer | Activation Function in the Hidden Layer | Activation Function in the Output Layer | Optimization Algorithm |
---|---|---|---|---|

Sa | 3 | Exponential | Logistic | BFGS 0 |

Spk | 2 | Tanh | Tanh | BFGS 45 |

Sk | 4 | Identity | Tanh | BFGS 3 |

Svk | 2 | Exponential | Exponential | BFGS 10 |

MRR | 3 | Logistic | Tanh | BFGS 50 |

Model | Values of Sensitivity | ||
---|---|---|---|

E | WS | t_{off} | |

Sa | 3.05 | 1.28 | 1.16 |

Spk | 6.35 | 5.43 | 1.91 |

Sk | 7.19 | 1.57 | 1.75 |

Svk | 5.14 | 1.08 | 1.40 |

MRR | 335.87 | 22.68 | 360.77 |

Model | Correlation Coefficient R | |||
---|---|---|---|---|

RSM | ANN | |||

Train | Test | Validation | ||

Sa | 0.96 | 0.97 | 0.98 | 0.99 |

Spk | 0.92 | 0.96 | 0.99 | 0.99 |

Sk | 0.93 | 0.95 | 0.97 | 0.98 |

Svk | 0.97 | 0.97 | 0.98 | 0.99 |

MRR | 0.99 | 0.99 | 0.99 | 0.99 |

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## Share and Cite

**MDPI and ACS Style**

Oniszczuk-Świercz, D.; Świercz, R.; Michna, Š. Evaluation of Prediction Models of the Microwire EDM Process of Inconel 718 Using ANN and RSM Methods. *Materials* **2022**, *15*, 8317.
https://doi.org/10.3390/ma15238317

**AMA Style**

Oniszczuk-Świercz D, Świercz R, Michna Š. Evaluation of Prediction Models of the Microwire EDM Process of Inconel 718 Using ANN and RSM Methods. *Materials*. 2022; 15(23):8317.
https://doi.org/10.3390/ma15238317

**Chicago/Turabian Style**

Oniszczuk-Świercz, Dorota, Rafał Świercz, and Štefan Michna. 2022. "Evaluation of Prediction Models of the Microwire EDM Process of Inconel 718 Using ANN and RSM Methods" *Materials* 15, no. 23: 8317.
https://doi.org/10.3390/ma15238317