# Generating Component Designs for an Improved NVH Performance by Using an Artificial Neural Network as an Optimization Metamodel

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## Abstract

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## 1. Introduction

## 2. Approach

#### 2.1. Use Case Scenario

#### 2.2. Workflow

#### 2.3. Artificial Neural Network

#### 2.4. Creation of the Target FRF

#### 2.5. Obtaining the New Parameter Set

#### 2.6. Process Verification

## 3. Application Examples

#### 3.1. Target FRF with Amplitude Reduction

#### 3.2. Maximum-Curve with Multiple Amplitude Optimization Targets

#### 3.3. Change of Eigenfrequency

#### 3.4. Combined Amplitude and Frequency Changes

#### 3.5. Comparison to Earlier Investigations

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANN | Artificial Neural Network |

FE | Finite Element |

FEM | Finite Element Method |

FRF | Frequency Response Function |

HL | Hidden Layer |

MSE | Mean Squared Error |

NVH | Noise, Vibration, and Harshness |

ReLu | Rectified Linear Unit |

SFLH | Space Filling Latin Hypercube |

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**Figure 1.**Knuckle of a vehicle suspension. The flat reddish surface in the center represents the wheel hub attachment surface. Gray spheres inside gray surfaces represent variable kinematic hard points. FRFs describe the noise transfer between each blue arrow and each red arrow. Each arrow represents one of the three directions ${x}_{1}$, ${x}_{2}$ or ${x}_{3}$.

**Figure 2.**Flow chart representing the presented approach. The simulated designs created via DoE serve as training data for multiple ANNs. The optimizer identifies fitting parameter sets that fulfill the target curves. The identified design is then validated.

**Figure 3.**User input for the creation of a target curve. A graphical application presents the original FRF (black) and the skyline of all FRFs of the DoE data set (gray). The design engineer draws (pen symbol) a desired target curve into the plot (blue).

**Figure 5.**Optimization using a matching-curve for a desired amplitude reduction around 1700 $\mathrm{Hz}$.

**Figure 6.**Optimization using a drawn maximum-curve describing a multi-objective optimization. Desired amplitude reduction at multiple frequency ranges while allowing small eigenfrequency shifts.

**Figure 7.**Optimization using a matching-curve to achieve an eigenfrequency raise at 1700 $\mathrm{Hz}$.

**Figure 8.**Optimization using a matching-curve to achieve an eigenfrequency reduction at 1900 $\mathrm{Hz}$.

**Figure 9.**Optimization using a matching-curve to achieve an eigenfrequency raise and an amplitude reduction at 1350 $\mathrm{Hz}$.

**Figure 10.**Optimization using a matching-curve to achieve an eigenfrequency reduction and an amplitude reduction at 1350 $\mathrm{Hz}$.

**Figure 11.**Optimization using a maximum-curve to achieve an eigenfrequency and amplitude reduction at multiple frequency ranges.

Layer | Size | Activation |
---|---|---|

In Layer ${d}_{\mathrm{IN}}$ | 15 | – |

Layer 1 ${d}_{\mathrm{HL}1}$ | 2^{10} | ReLU |

Layer 2 ${d}_{\mathrm{HL}2}$ | 2^{10} | ReLU |

Layer 3 ${d}_{\mathrm{HL}3}$ | 2^{10} | ReLU |

Out Layer ${d}_{\mathrm{OUT}}$ | 1000 | Identity |

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

Batch size | 10 |

Epochs | 200 |

Optimizer | Adam |

Loss | MSE |

Dropout ${d}_{\mathrm{HL}1}$, ${d}_{\mathrm{HL}2}$ | 20% |

Dropout ${d}_{\mathrm{HL}3}$ | 40% |

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**MDPI and ACS Style**

von Wysocki, T.; Rieger, F.; Tsokaktsidis, D.E.; Gauterin, F. Generating Component Designs for an Improved NVH Performance by Using an Artificial Neural Network as an Optimization Metamodel. *Designs* **2021**, *5*, 36.
https://doi.org/10.3390/designs5020036

**AMA Style**

von Wysocki T, Rieger F, Tsokaktsidis DE, Gauterin F. Generating Component Designs for an Improved NVH Performance by Using an Artificial Neural Network as an Optimization Metamodel. *Designs*. 2021; 5(2):36.
https://doi.org/10.3390/designs5020036

**Chicago/Turabian Style**

von Wysocki, Timo, Frank Rieger, Dimitrios Ernst Tsokaktsidis, and Frank Gauterin. 2021. "Generating Component Designs for an Improved NVH Performance by Using an Artificial Neural Network as an Optimization Metamodel" *Designs* 5, no. 2: 36.
https://doi.org/10.3390/designs5020036