# Artificial Neural Network and Response Surface Methodology Based Analysis on Solid Particle Erosion Behavior of Polymer Matrix Composites

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## Abstract

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_{s}) are used to analyze the bonding behavior of reinforcement and matrix against the natural abrasive slurry. The response surface methodology is adopted to analyze the effect of various erosion parameters on the erosion resistance. The slurry pressure, impingement angle and nozzle diameter, were used as erosion parameters whereas erosion loss, i.e., weight loss during an erosion phenomenon was considered as a response parameter. The artificial neural network model was used to validate the attained outcomes for an optimum solution. The comparative analysis of response surface methodology (RSM) and artificial neural network (ANN) models shows good agreement with the erosion behavior of glass fiber reinforced polymer matrix composites.

## 1. Introduction

## 2. Materials and Methods

_{1}, and N

_{o}are values at level 1, and level 0 whereas N

_{K}is actual parametric value to level interest.

## 3. Response Surface Methodology

_{0}and b

_{i}are second-order regression coefficients and b

_{ii}and b

_{ij}represents a quadratic effect. K represents several machining parameters and x

_{i}and x

_{j}represents terms, which deal with the effect of machining parameters.

## 4. Artificial Neural Network

## 5. Results

#### 5.1. Parametric Evaluation through RSM

#### 5.2. Modeling Through ANN

## 6. Discussion

## 7. Conclusions

- The erosion during the solid particle impact is deeply affected by the impingement angle. The maximum erosion occurred at an angle of 60°, which means the composite lay in the category of semi ductile materials.
- From the ANOVA table for erosion, the most significant and influential parameter was found to be the impingement angle. Additionally, the generated quadratic models were suitably fitted with investigational results.
- The SEM analysis of the river sand particles shows the irregular and sharp conical edges, which were responsible for the high erosion rate.
- The SEM analysis of composite surface shows that the impingement angle of 60° degraded the upper layer of the composite very finely and exposed the fibers, which caused an excess material loss in comparison to a 30° and 90° impingement angle.
- MATLAB’s neural network fitting app was used for generating a network model, which produced good comparative results by using hidden layers and neurons. The developed model showed 0.43% deviation with the results obtained from RSM based model.
- The multiple hidden layers signified an arbitrary decision boundary to arbitrary accuracy with rational activation function and provided precise result with minimal deviation in comparison to the RSM model.
- The comparative analysis showed that the ANN model could be used proficiently for the validation of single response optimized results obtained during solid particle erosion of polymer matrix composites.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) Response surface plots for slurry pressure and nozzle diameter on erosion. (

**b**) Response surface plots for slurry pressure and impingement angle on erosion. (

**c**) Response surface plots for nozzle diameter and impingement angle on erosion.

**Figure 9.**(

**a**) SEM of erosion at a 30° impingement angle, (

**b**) SEM of erosion at a 60° impingement angle and (

**c**) SEM of erosion at a 30° impingement angle.

Symbol | Erosion Parameters | Level 1 | Level 2 | Level 3 |
---|---|---|---|---|

P | Slurry Pressure (Psi) | 60 | 75 | 90 |

N | Nozzle Diameter (mm) | 2.0 | 2.5 | 3.0 |

I | Impingement Angle (°) | 30 | 60 | 90 |

Exp. No. | Slurry Pressure (Psi) | Coded Value | Nozzle Diameter (mm) | Coded Value | Impingement Angle (⸰) | Coded Value | Mean Erosion (mg/min) |
---|---|---|---|---|---|---|---|

1 | 75 | 0 | 2.5 | 0 | 60 | 0 | 2.229 |

2 | 75 | 0 | 2.5 | 0 | 60 | 0 | 2.325 |

3 | 75 | 0 | 2 | −1 | 90 | 1 | 2.117 |

4 | 75 | 0 | 3 | 1 | 90 | 1 | 2.113 |

5 | 90 | 1 | 2 | −1 | 60 | 0 | 2.351 |

6 | 60 | −1 | 3 | 1 | 60 | 0 | 2.311 |

7 | 75 | 0 | 2 | −1 | 30 | −1 | 1.984 |

8 | 75 | 0 | 2.5 | 0 | 60 | 0 | 2.315 |

9 | 90 | 1 | 2.5 | 0 | 30 | −1 | 1.993 |

10 | 60 | −1 | 2.5 | 0 | 90 | 1 | 2.101 |

11 | 90 | 1 | 3 | 1 | 60 | 0 | 2.345 |

12 | 75 | 0 | 2.5 | 0 | 60 | 0 | 2.334 |

13 | 60 | −1 | 2 | −1 | 60 | 0 | 2.342 |

14 | 90 | 1 | 2.5 | 0 | 90 | 1 | 2.113 |

15 | 60 | −1 | 2.5 | 0 | 30 | −1 | 1.982 |

16 | 75 | 0 | 3 | 1 | 30 | −1 | 1.989 |

17 | 75 | 0 | 2.5 | 0 | 60 | 0 | 2.361 |

Source | Sum of Squares | df | Mean Square | F Value | p-Value | Remarks |
---|---|---|---|---|---|---|

Model | 0.35 | 9 | 0.039 | 26.83 | 0.0001 | Significant |

A-P | 5.445 × 10^{−4} | 1 | 5.445 × 10^{−4} | 0.37 | 0.5607 | |

B-N | 1.620 × 10^{−4} | 1 | 1.620 × 10^{−4} | 0.11 | 0.7488 | |

C-I | 0.031 | 1 | 0.031 | 21.06 | 0.0025 | |

AB | 1.563 × 10^{−4} | 1 | 1.563 × 10^{−4} | 0.11 | 0.7531 | |

AC | 2.500 × 10^{−7} | 1 | 2.500 × 10^{−7} | 0.001712 | 0.9899 | |

BC | 2.025 × 10^{−5} | 1 | 2.025 × 10^{−5} | 0.014 | 0.9096 | |

A2 | 4.620 × 10^{−4} | 1 | 4.620 × 10^{−4} | 0.32 | 0.5913 | |

B2 | 8.223 × 10^{−4} | 1 | 8.223 × 10^{−4} | 0.56 | 0.4774 | |

C2 | 0.32 | 1 | 0.32 | 219.73 | <0.0001 | |

Residual | 0.010 | 7 | 1.460 × 10^{−3} | |||

Lack of Fit | 2.710 × 10^{−4} | 3 | 9.033 × 10^{−5} | 0.036 | 0.9894 | Not Significant |

Pure Error | 9.949 × 10^{−3} | 4 | 2.487 × 10^{−3} | |||

Cor Total | 0.36 | 16 |

Phases | Sample | MSE | R |
---|---|---|---|

Training | 11 | 3.18611 × 10^{−4} | 9.93792 × 10^{−1} |

Validation | 3 | 5.16810 × 10^{−3} | 9.61107 × 10^{−1} |

Testing | 3 | 8.59712 × 10^{−3} | 7.60270 × 10^{−1} |

**Table 5.**Comparative analysis on response surface methodology (RSM) and artificial neural network (ANN).

Model | Parametric Values | Erosion | Deviation |
---|---|---|---|

RSM | [75;2.5;60] | 2.325 | 0.43% |

ANN | [75;2.5;60] | 2.324 |

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**MDPI and ACS Style**

Antil, S.K.; Antil, P.; Singh, S.; Kumar, A.; Pruncu, C.I.
Artificial Neural Network and Response Surface Methodology Based Analysis on Solid Particle Erosion Behavior of Polymer Matrix Composites. *Materials* **2020**, *13*, 1381.
https://doi.org/10.3390/ma13061381

**AMA Style**

Antil SK, Antil P, Singh S, Kumar A, Pruncu CI.
Artificial Neural Network and Response Surface Methodology Based Analysis on Solid Particle Erosion Behavior of Polymer Matrix Composites. *Materials*. 2020; 13(6):1381.
https://doi.org/10.3390/ma13061381

**Chicago/Turabian Style**

Antil, Sundeep Kumar, Parvesh Antil, Sarbjit Singh, Anil Kumar, and Catalin Iulian Pruncu.
2020. "Artificial Neural Network and Response Surface Methodology Based Analysis on Solid Particle Erosion Behavior of Polymer Matrix Composites" *Materials* 13, no. 6: 1381.
https://doi.org/10.3390/ma13061381