# Classification of Chaotic Squeak and Rattle Vibrations by CNN Using Recurrence Pattern

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## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Results

## 4. Discussion and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 4.**Dynamic solutions for the Rossler model for various $c$: (

**a**) time analysis; (

**b**) 3-D phase portrait.

**Figure 7.**Chaotic analysis for Rossler model (

**a**) bifurcation diagram of displacement (

**b**) and largest Lyapunov exponent with respect to $c$.

**Figure 9.**Results of the numerical experiment for the Rossler model: (

**a**) accuracy; (

**b**) and loss curves over 100 epochs.

**Figure 11.**Chaotic analysis for the S&R model: (

**a**) bifurcation diagram of displacements; (

**b**) largest Lyapunov exponent, for rattle model with respect to $\eta $; (

**c**) bifurcation diagram of displacements; (

**d**) largest Lyapunov exponent, for single-mode squeak model with respect to $\eta $; (

**e**) bifurcation diagram of displacements; (

**f**) largest Lyapunov exponent, for multi-modes squeak model with respect to $\sigma $.

**Figure 12.**Dynamic solutions for the rattle model for various $\eta $: (

**a**) time analysis; (

**b**) phase portrait corresponding to (

**a**).

**Figure 13.**Dynamic solutions for single-mode squeak model for various $\eta $: (

**a**) time analysis; (

**b**) phase portrait corresponding to (

**a**).

**Figure 14.**Dynamic solutions for single-mode squeak model for various $\sigma $: (

**a**) time analysis; (

**b**) phase portrait corresponding to (

**a**).

**Figure 16.**Results of the numerical experiment for the S&R model: (

**a**) accuracy; (

**b**) and loss curves over 100 epochs.

Layer (Type) | Output Shape | Param # |
---|---|---|

Conv2d | (None, 200, 200, 32) | 896 |

Batch normalization | (None, 200, 200, 32) | 128 |

Max pooling 2d | (None, 100, 100, 32) | 0 |

Conv2d_1 | (None, 100, 100, 64) | 18,496 |

Batch normalization_1 | (None, 100, 100, 64) | 256 |

Max pooling 2d_1 | (None, 50, 50, 64) | 0 |

Conv2d_2 | (None, 50, 50, 128) | 73,856 |

Batch normalization_2 | (None, 50, 50, 128) | 512 |

Max pooling 2d_2 | (None, 25, 25, 128) | 0 |

Conv2d_3 | (None, 25, 25, 256) | 295,168 |

Batch normalization_3 | (None, 25, 25, 256) | 1024 |

Max pooling 2d_3 | (None, 12, 12, 256) | 0 |

Conv2d_4 | (None, 12, 12, 512) | 1,180,160 |

Global Average Pooling 2d | (None, 512) | 0 |

Dense | (None, 2) | 1026 |

Data | Percentage | Number of Samples |
---|---|---|

Training | 56% | 2240 |

Validation | 14% | 560 |

Testing | 30% | 1200 |

Data | Percentage | Number of Samples |
---|---|---|

Training | 56% | 4160 |

Validation | 14% | 1040 |

Testing | 30% | 1800 |

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**MDPI and ACS Style**

Nam, J.; Kang, J.
Classification of Chaotic Squeak and Rattle Vibrations by CNN Using Recurrence Pattern. *Sensors* **2021**, *21*, 8054.
https://doi.org/10.3390/s21238054

**AMA Style**

Nam J, Kang J.
Classification of Chaotic Squeak and Rattle Vibrations by CNN Using Recurrence Pattern. *Sensors*. 2021; 21(23):8054.
https://doi.org/10.3390/s21238054

**Chicago/Turabian Style**

Nam, Jaehyeon, and Jaeyoung Kang.
2021. "Classification of Chaotic Squeak and Rattle Vibrations by CNN Using Recurrence Pattern" *Sensors* 21, no. 23: 8054.
https://doi.org/10.3390/s21238054