# Aerodynamics Optimization of Multi-Blade Centrifugal Fan Based on Extreme Learning Machine Surrogate Model and Particle Swarm Optimization Algorithm

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## Abstract

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## 1. Introduction

## 2. Optimization Problem Definition and Description

#### 2.1. Optimization Object

#### 2.2. Optimization Model

#### 2.3. Flowchart of Blade Parameter Optimization

## 3. The Surrogate Model and Optimization Algorithm

#### 3.1. ELM Surrogate Model

#### 3.2. Particle Swarm Optimization

#### 3.3. Extreme Learning Machine Based on PSO

- Preprocessing of experimental data. The experimental data are divided into training sets and test sets, and then normalized.
- The parameters of particle swarm optimization are transformed into ELM parameters, and then the input and output samples are sent to ELM for prediction and the fitness is calculated.
- The individual and global extremums for all particles are calculated.
- According to the formula of particle renewal speed and position, the particle velocity, position, and weight are updated.
- When the number of iterations reaches the maximum number of iterations set or the fitness meets the requirements, the search is stopped; otherwise, the iterations are repeated until the condition of stopping iterations is reached.
- The PSO-ELM model is completed. The particle position corresponding to the optimal individual is the optimal weights and thresholds of the ELM network, which are substituted into the ELM model.

## 4. Concrete Optimization Process and Results

#### 4.1. Optimization Structural Model

#### 4.2. CFX Simulation

#### 4.3. Design of Simulation Experiment

## 5. Results and Discussion

## 6. Conclusions

- Using the CFD method to solve aerodynamic performance is complex and time-consuming. The PSO-ELM surrogate model set as the fitness function is used in the PSO optimization process. From the evaluation index ${R}^{2}$, the ${R}^{2}$ value is equal to 0.99973 for the PSO-ELM model and the ${R}^{2}$ value is equal to 0.96299 for the ELM model; the accuracy of the PSO-ELM surrogate model has increased.
- The total pressure is improved from 140.6 Pa to 151 Pa after optimization using simulation experiment design and the PSO algorithm.
- This paper applied the modified ELM model to the optimal design of the multi-blade centrifugal fan and verifies the feasibility of coupling the modified ELM model and PSO algorithm to the blade parametric design. It provides new ideas for the optimal design of multi-blade centrifugal fans and other centrifugal fans. The entire optimization design has certain engineering use value.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Reference | Optimization Parameter | Method |
---|---|---|

Xu et al. [1] | Groove width, groove depth, groove center distance, groove number, different groove shapes | CFD simulation design method |

Ye et al. [2] | Inner diameter, bevel-cutting blade | CFD technology, test |

Li et al. [3] | Vortex characteristics | CFD technology |

Wei et al. [4] | Clearance, the inclination angle, the volute tongue | CFD technology, test |

Zhou et al. [5,6,7] | Multi-blade centrifugal fan blade airfoil parameter | 1. CST function parameterization 2. Latin hypercube sampling 3. RBF model 4. Non-dominant sorting genetic algorithm-II |

Alla et al. [8,9] | Multi-blade centrifugal fan impeller and wheel parameter | 1. Latin hypercube sampling 2. Response surface approximation model 3. EGO approach |

Heo et al. [10] | The scroll cut-off angle, the scroll diffuser expansion angle, the diameter ratio of the impeller, the blade exit angle | 1. Latin hypercube sampling 2. Kriging surrogate model 3. Algorithm-II |

Le et al. [11] | Research operating condition on the centrifugal fan performance and flow characteristics, obtaining the topology optimization design | ANSYS software |

Kim et al. [12] | Location of cutoff, radius of cutoff, width of impeller, flow coefficient | Numerical analysis, response surface optimization method |

Structural Parameters | Value (mm) |
---|---|

Height | 180 |

Width | 61 |

Length | 171 |

Diameter | 133 |

Inlet diameter | 110 |

Outlet parameter | 59 × 71 |

Sequence | Position Parameter/° | Shape Parameter/° | Total Pressure/Pa |
---|---|---|---|

1 | 0 | 0 | 49.73 |

2 | 0 | 10 | 69.41 |

3 | 0 | 20 | 91.23 |

4 | 0 | 30 | 106.10 |

5 | 0 | 40 | 99.23 |

6 | 10 | 0 | 50.32 |

7 | 10 | 10 | 77.76 |

8 | 10 | 20 | 110.20 |

9 | 10 | 30 | 129.80 |

10 | 10 | 40 | 140.60 |

11 | 20 | 0 | 49.05 |

12 | 20 | 10 | 71.45 |

13 | 20 | 20 | 119.20 |

14 | 20 | 30 | 134.20 |

15 | 20 | 40 | 150.10 |

16 | 30 | 0 | 43.04 |

17 | 30 | 10 | 70.02 |

18 | 30 | 20 | 103.91 |

19 | 30 | 30 | 109.7 |

20 | 30 | 40 | 130.90 |

21 | 40 | 0 | 30.27 |

22 | 40 | 10 | 74.29 |

23 | 40 | 20 | 101.10 |

24 | 40 | 30 | 86.80 |

25 | 40 | 40 | 80.35 |

Evaluation Index | PSO-ELM | ELM |
---|---|---|

${R}^{2}$ | 0.99973 | 0.96299 |

Centrifugal Fan | Blade Parameters [pp sp]/(°) | Total Pressure/(Pa) |
---|---|---|

Before optimization | (10.0, 40.0) | 140.6 |

After optimization | (18.0, 39.0) | 151 |

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**MDPI and ACS Style**

Meng, F.; Wang, L.; Ming, W.; Zhang, H.
Aerodynamics Optimization of Multi-Blade Centrifugal Fan Based on Extreme Learning Machine Surrogate Model and Particle Swarm Optimization Algorithm. *Metals* **2023**, *13*, 1222.
https://doi.org/10.3390/met13071222

**AMA Style**

Meng F, Wang L, Ming W, Zhang H.
Aerodynamics Optimization of Multi-Blade Centrifugal Fan Based on Extreme Learning Machine Surrogate Model and Particle Swarm Optimization Algorithm. *Metals*. 2023; 13(7):1222.
https://doi.org/10.3390/met13071222

**Chicago/Turabian Style**

Meng, Fannian, Liujie Wang, Wuyi Ming, and Hongxiang Zhang.
2023. "Aerodynamics Optimization of Multi-Blade Centrifugal Fan Based on Extreme Learning Machine Surrogate Model and Particle Swarm Optimization Algorithm" *Metals* 13, no. 7: 1222.
https://doi.org/10.3390/met13071222