# Performance Improvement of Human Centrifuge Systems through Multi-Objective Configurational Design Optimisation

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. HCS Configurational Design

#### 1.2. Paper Contributions

## 2. Kinematic and Dynamic Model of a Four-Axis Human Centrifuge System

#### 2.1. Inverse Kinematic Analysis

#### 2.2. Inverse Dynamic Analysis

## 3. Problem Formulation

#### 3.1. Objective Functions

#### 3.2. Design Parameters and Constraints

#### 3.3. Formulation of the Optimisation Problem

## 4. Configurational Design Optimisation Method

#### 4.1. Optimisation Solver Parameters

#### 4.2. Human Centrifuge System Parameters

## 5. Optimisation Results

## 6. Discussion

## 7. Future Developments

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Trajectories of the Barrel Roll (M1), Loop (M2), and High Yo-Yo (M3) Aircraft Combat Manoeuvres.

**Figure 6.**Multi-objective optimisation for the Barrel Roll manoeuvre. (

**a**) The effect of arm length on Coriolis, FHAR, and cost index. (

**b**) The distribution of optimal solutions for seat x, y, and z positions.

**Figure 7.**Multi-objective optimisation for the Loop manoeuvre. (

**a**) The effect of arm length on Coriolis, FHAR, and cost index. (

**b**) The distribution of optimal solutions for seat x, y, and z positions.

**Figure 8.**Multi-objective optimisation for the High Yo-Yo manoeuvre. (

**a**) The effect of arm length on Coriolis, FHAR, and cost index. (

**b**) The distribution of optimal solutions for seat x, y, and z positions.

**Figure 9.**Multi-objective optimisation for all three manoeuvres. (

**a**) The effect of arm length on Coriolis, FHAR, and cost index. (

**b**) The distribution of optimal solutions for seat x, y, and z positions.

**Figure 10.**Comparison of the optimum and generally selected configurational design parameters, (

**a**) comparison of the Coriolis acceleration, and (

**b**) comparison of the FHAR.

Optimisation Trial | Aircraft Manoeuvre | Objectives |
---|---|---|

1 | Barrel Roll | Coriolis/FHAR/ Cost Index |

2 | Loop | |

3 | High Yo-Yo | |

4 | All combined |

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

Maximum Iterations | 100 |

Optimality Tolerance | 0.001 |

Step Tolerance | 0.05 |

Function Tolerance | 0.05 |

Constraint Tolerance | 0.001 |

Optimisation Parameters | Values |
---|---|

Population Size | 100 |

Crossover Fraction | 0.8 |

Migration Fraction | 0.2 |

Pareto Fraction | 0.35 |

Generations Limit | 100 |

Stall Generations Limit | 50 |

Function Tolerance | $1\times {10}^{-4}$ |

Estimated Computation Time | 6 h |

Body Part | Displacement from Seat Body Frame (m) | ||
---|---|---|---|

x-Axis | y-Axis | z-Axis | |

Head | 0 | 0 | 0.75 |

Feet | 0.65 | 0 | −0.54 |

Chest | 0 | 0 | 0.45 |

Objective | Optimal Value | Corresponding Design Parameters | |||
---|---|---|---|---|---|

Arm Length (m) | Seat Position (m) | ||||

x | y | z | |||

Coriolis Acc (G) | 0.017 | 17.997 | 0.112 | −0.452 | −0.832 |

FHAR | 1.008 | 17.988 | 0.145 | −0.444 | −0.824 |

Cost Index | 0.576 | 5.028 | 0.367 | 0.425 | −1.242 |

Objective | Optimal Value | Corresponding Design Parameters | |||
---|---|---|---|---|---|

Arm Length (m) | Seat Position (m) | ||||

x | y | z | |||

Coriolis Acc (G) | 0.033 | 16.815 | 0.079 | 0.047 | −0.821 |

FHAR | 1.025 | 17.200 | 0.470 | 0.443 | −1.072 |

Cost Index | 0.864 | 5.049 | 0.468 | −0.050 | −1.213 |

Objective | Optimal Value | Corresponding Design Parameters | |||
---|---|---|---|---|---|

Arm Length (m) | Seat Position (m) | ||||

x | y | z | |||

Coriolis Acc (G) | 0.024 | 16.643 | −0.019 | −0.228 | −0.713 |

FHAR | 1.015 | 17.598 | 0.464 | −0.155 | −0.621 |

Cost Index | 0.517 | 5.039 | −0.115 | 0.407 | −1.012 |

Objective | Optimal Value | Corresponding Design Parameters | |||
---|---|---|---|---|---|

Arm Length (m) | Seat Position (m) | ||||

x | y | z | |||

Coriolis Acc (G) | 0.055 | 8.174 | 0.020 | −0.170 | −0.803 |

FHAR | 1.056 | 8.637 | 0.110 | −0.088 | −0.946 |

Cost Index | 1.334 | 6.157 | 0.224 | −0.244 | −0.930 |

Trial | Minimised Objective | Arm Length (m) | Seat Position (m) [x, y, z] | Max Error (G) [Gx, Gy, Gz] | RMS Error (G) [Gx, Gy, Gz] |
---|---|---|---|---|---|

1 | Coriolis Acc | 17.997 | [0.112, −0.452, −0.832] | [0.045, 0.038, 0.183] | [0.013, 0.010, 0.025] |

FHAR | 17.988 | [0.145, −0.444, −0.824] | [0.044, 0.038, 0.282] | [0.012, 0.010, 0.025] | |

Cost Index | 5.028 | [0.367, 0.425, −1.242] | [0.311, 0.966, 0.899] | [0.053, 0.046, 0.094] | |

2 | Coriolis Acc | 16.815 | [0.079, 0.047, −0.821] | [0.041, 0.025, 0.201] | [0.014, 0.008, 0.026] |

FHAR | 17.200 | [0.470, 0.443, −1.072] | [0.097, 0.044, 0.269] | [0.016, 0.011, 0.025] | |

Cost Index | 5.049 | [0.468, −0.050, −1.213] | [0.549, 1.763, 2.286] | [0.047, 0.047, 0.124] | |

3 | Coriolis Acc | 16.643 | [−0.019, −0.228, −0.713] | [0.027, 0.035, 0.190] | [0.013, 0.010, 0.026] |

FHAR | 17.598 | [0.464, −0.155, −0.621] | [0.029, 0.032, 0.189] | [0.012, 0.010, 0.026] | |

Cost Index | 5.039 | [−0.115, 0.407, −1.012] | [0.625, 1.094, 1.428] | [0.055, 0.046, 0.125] | |

4 | Coriolis Acc | 8.174 | [0.020, −0.170, −0.803] | [0.048, 0.032, 0.262] | [0.019, 0.012, 0.036] |

FHAR | 8.637 | [0.110, −0.088, −0.946] | [0.086, 0.025, 0.214] | [0.020, 0.011, 0.035] | |

Cost Index | 6.157 | [0.224, −0.244, −0.930] | [0.180, 0.608, 0.911] | [0.029, 0.026, 0.046] |

**Table 10.**Comparison of objective values for the optimum and generally selected configurational design parameters.

Objective | Optimal Design RMS Error | General Design RMS Error |
---|---|---|

Coriolis (G) | 0.0216 | 0.0245 |

FHAR | 0.0185 | 0.0273 |

HCS Parameter | Value |
---|---|

HCS arm length (m) | 5 |

Seat offset from the gondola CoR (m) [x, y, z] | [−0.5, 0, −0.80] |

Displacement of user’s chest CoM from the seat BF (m) [x, y, z] | [0, 0, 0.45] |

Gondola Rotation | Minimised Objective | Rotation Parameters | |||
---|---|---|---|---|---|

Min (deg) | Max (deg) | RoM (deg) | Max RPM | ||

Roll | Coriolis | −89.7 | 49.5 | 139.2 | 48.8 |

FHAR | −89.7 | 49.5 | 139.2 | 48.8 | |

Cost Index | −86.5 | 48.2 | 134.7 | 48.5 | |

Pitch | Coriolis | 0 | 86.7 | 86.7 | 70.4 |

FHAR | 0 | 86.7 | 86.7 | 70 | |

Cost Index | −1.4 | 78.5 | 79.8 | 205.5 | |

Yaw | Coriolis | −28.2 | 85.5 | 113.6 | 44.6 |

FHAR | −28.3 | 85.6 | 113.8 | 45.4 | |

Cost Index | −17.1 | 78.1 | 95.2 | 70 |

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**MDPI and ACS Style**

Winter, A.; Mohajer, N.; Nahavandi, D.; Mohamed, S.
Performance Improvement of Human Centrifuge Systems through Multi-Objective Configurational Design Optimisation. *Aerospace* **2023**, *10*, 1013.
https://doi.org/10.3390/aerospace10121013

**AMA Style**

Winter A, Mohajer N, Nahavandi D, Mohamed S.
Performance Improvement of Human Centrifuge Systems through Multi-Objective Configurational Design Optimisation. *Aerospace*. 2023; 10(12):1013.
https://doi.org/10.3390/aerospace10121013

**Chicago/Turabian Style**

Winter, Asher, Navid Mohajer, Darius Nahavandi, and Shady Mohamed.
2023. "Performance Improvement of Human Centrifuge Systems through Multi-Objective Configurational Design Optimisation" *Aerospace* 10, no. 12: 1013.
https://doi.org/10.3390/aerospace10121013