# Multi-Objective Optimization of the Process Parameters of a Grinding Robot Using LSTM-MLP-NSGAII

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Mathematical Model of Surface Roughness

_{g}is the capacity of the pneumatic motor, Pr is the spindle pressure, η is the volumetric efficiency, q

_{v}is the flow rate. According to the Bernoulli equation in fluid dynamics, q

_{v}can be expressed by the following equation

_{T}is the cross-sectional area of the pipes, $\rho $ is the density of air. Substituting Equations (2) to (5) into (1) yields:

_{o}in Equation (7), and the static variable representing the structural property is integrated as Q

_{o}in Equation (8). The simplified surface roughness Equation (6) is obtained by combining the constant C

_{o}and the structural property term Q

_{o}, obtaining a mathematical model for the relationship between the PPGR and the quality of Ra.

#### 2.2. Algorithm for Multi-Objective Optimization

#### 2.2.1. LSTM Model for Fitting the Surface Roughness

#### 2.2.2. MLP Model for Fitting the Grinding Time

#### 2.2.3. NSGA-II for Multi-Objective Optimization

_{0}of size N was generated, and using the tournament selection algorithm, crossover and mutation were performed to obtain the offspring Q

_{0}, which was combined into a population R

_{0}. Then, iteration through all the solutions in the population R

_{0}was carried out, the number of dominated sets was computed for each solution for a fast non-dominated sorting, and the fitness values of each level of non-dominated solutions in the sorted Z

_{1}, Z

_{2}, Z

_{3}were assigned according to their frontier levels. In this case, the solutions in the first level of the non-dominated frontier Z

_{1}were the best solutions, and all the solutions in this level were retained in the new-generation population P

_{1}according to the elitism strategy. If the number of Z

_{1}is less than N, the next level of non-dominated solutions in level Z

_{2}is selected to complement them, until the number of remaining solutions in the P

_{1}population is not sufficient to merge all solutions within a complete non-dominated frontier level. The solutions in the last set of nondominated solutions that cannot be merged into the P

_{1}population are sorted by crowded distance. The sorted top solution were selected to complement the remaining P

_{1}population to reach N. P

_{1}was selected with a crowded comparison operator through the tournament selection algorithm, and Q

_{1}was generated using the traditional GA algorithm with crossover and mutation. P

_{1}and Q

_{1}were combined for the R

_{1}population, and the operation of the fast nondominated sorting was repeated until the number of iteration generations was reached.

_{t+1}of the new generation was obtained by calculating the crowding distance. The new offspring population Q

_{t+1}was obtained using the genetic algorithm based on the elitist strategy, and the above steps were repeated. After continuous selection, mutation, crossover and iteration to reach the number of generations set by the algorithm, the optimal Pareto front was obtained.

## 3. Experiment and Method Implementation

#### 3.1. Experiment Platform

#### 3.2. Experiment Dataset

#### 3.3. LSTM and MLP Neural Network Training

#### 3.4. Surface Roughness and Grinding Time Prediction

## 4. Optimization and Validation of the Process Parameters

## 5. Discussion and Conclusions

- Based on the mechanism of the rotary burrs and the driving characteristics of the RCMRT, a model for the qualitative relationship between surface quality of a robotic pneumatic grinding system, robot speed, radial compliance force and spindle air pressure was presented.
- The proposed LSTM-MLP-NSGAII model considers the effects of burr wear and robot kinematics on grinding quality and time in an integrated approach compared to traditional methods that rely on manual experience.
- A multi-objective optimization method for the PPGR is proposed, taking surface roughness and grinding time into account for the first time.
- Compared with the manual empirical method, the Ra achieved was at least 13.62% better than that obtained with the manual empirical method, and the grinding time was reduced by 28%.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Experimental training results. (

**a**) Loss of the LSTM network; (

**b**) lLoss of the MLP network.

**Figure 9.**Experimental prediction results. (

**a**) Average surface roughness Ra prediction results; (

**b**) grinding time prediction results.

Trial Group | Burrs No. | f (mm/s) | Pz (MPa) | Test Group | Pr (MPa) | |||||
---|---|---|---|---|---|---|---|---|---|---|

Min. | Max. | Step | Min. | Max. | Step | f (mm/s) | Pz (MPa) | |||

1 | B1 | 25 | 300 | 25 | 0.2 | 0.4 | 0.05 | 50 | 0.2 | 0.2 |

B2 | 0.25 | |||||||||

B3 | 0.35 | |||||||||

2 | B4 | 25 | 300 | 25 | 0.2 | 0.4 | 0.05 | 50 | 0.2 | 0.3 |

B5 | 0.25 | |||||||||

B6 | 0.35 | |||||||||

3 | B7 | 25 | 300 | 25 | 0.2 | 0.4 | 0.05 | 50 | 0.2 | 0.4 |

B8 | 0.25 | |||||||||

B9 | 0.35 | |||||||||

4 | B10 | 25 | 300 | 25 | 0.2 | 0.4 | 0.05 | 50 | 0.2 | 0.45 |

B11 | 0.25 | |||||||||

B12 | 0.35 |

Parameters | Value | |
---|---|---|

LSTM | MLP | |

Input shape | (25,3) | (25,3) |

Label shape | (25,1) | (25,1) |

Batch Size | 300 | 300 |

Number of input layer neurons | 64 | 32 |

Number of hidden layer neurons | 128 | 64,128 |

Number of output layer neurons | 1 | 1 |

Maximum epoch | 200 | 200 |

Optimizer | Adam | Adam |

Loss Function | MSE | MSE |

Activation Function | Sigmoid | Relu |

**Table 3.**Results of the comparison between the multi-objective optimization and manual experience methods.

Group | No | f (mm/s) | Pz (MPa) | Pr (MPa) | Ra (μm) | Time (s) | Ra Rate | Time Rate |
---|---|---|---|---|---|---|---|---|

Optimization | 21 | 108 | 0.25 | 0.3 | 0.246 | 6.703 | −52.32% | +0.04% |

22 | 152 | 0.2 | 0.35 | 0.506 | 6.687 | −43.65% | −47.33% | |

23 | 299 | 0.25 | 0.4 | 0.350 | 2.699 | −34.21% | −0.77% | |

24 | 240 | 0.3 | 0.3 | 0.298 | 3.095 | −13.62% | +54.01% | |

25 | 269 | 0.3 | 0.35 | 0.135 | 3.100 | −92.16% | −53.83% | |

26 | 290 | 0.25 | 0.35 | 0.165 | 3.091 | −66.74% | −16.46% | |

Manual Experience | 45 | 100 | 0.35 | 0.35 | 0.515 | 6.700 | - | - |

46 | 70 | 0.3 | 0.2 | 0.898 | 12.696 | |||

47 | 260 | 0.35 | 0.25 | 0.532 | 2.720 | |||

48 | 270 | 0.3 | 0.3 | 0.345 | 2.711 | |||

49 | 90 | 0.4 | 0.4 | 1.721 | 6.715 | |||

50 | 200 | 0.4 | 0.35 | 0.496 | 3.700 |

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**MDPI and ACS Style**

Li, R.; Wang, Z.; Yan, J.
Multi-Objective Optimization of the Process Parameters of a Grinding Robot Using LSTM-MLP-NSGAII. *Machines* **2023**, *11*, 882.
https://doi.org/10.3390/machines11090882

**AMA Style**

Li R, Wang Z, Yan J.
Multi-Objective Optimization of the Process Parameters of a Grinding Robot Using LSTM-MLP-NSGAII. *Machines*. 2023; 11(9):882.
https://doi.org/10.3390/machines11090882

**Chicago/Turabian Style**

Li, Ruizhi, Zipeng Wang, and Jihong Yan.
2023. "Multi-Objective Optimization of the Process Parameters of a Grinding Robot Using LSTM-MLP-NSGAII" *Machines* 11, no. 9: 882.
https://doi.org/10.3390/machines11090882