# Model-Free Data Mining of Families of Rotating Machinery

^{*}

## Abstract

**:**

## 1. Introduction

#### Background

## 2. The Harmonic Feature Space

## 3. Statistical Significance and Reduction

## 4. Clustering and Classification

## 5. Case Study

## 6. Conclusions and Future Works

## Author Contributions

## Funding

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**The Fourier transform bins of the z-axis of 1800 recordings all computed using the same FFT transform parameters.

**Figure 2.**The Fourier transform bins of the z-axis of the same 1800 recordings as Figure 1 now aligned in the harmonic feature space.

**Figure 4.**Dendrogram, same 6 machines as in Figure Table 3, colour indicates machine.

**Figure 5.**Family tree of 1800 recordings presented as heat map. Columns of equal colour represent clusters.

**Table 1.**The confusion matrix for data from six types of machines classified by SVM, to show separability.

0 | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|

M1.F1 | 18 | 2 | ||||

M2.F2 | 1 | 16 | ||||

M3.F3 | 5 | 16 | ||||

M4.F3 | 3 | 11 | ||||

M5.F4 | 2 | 8 | ||||

M6.F4 | 2 | 10 |

0 | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|

M1.F1 | 20 | |||||

M2.F2 | 17 | |||||

M3.F3 | 19 | 2 | ||||

M4.F3 | 1 | 11 | 2 | |||

M5.F4 | 10 | |||||

M6.F4 | 2 | 6 | 4 |

**Table 3.**The confusion matrix for data from six types of machines clustered into ten clusters as determined by optimizing the symmetric conditioned entropy.

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
---|---|---|---|---|---|---|---|---|---|---|

M1.F1 | 20 | |||||||||

M2.F2 | 17 | |||||||||

M3.F3 | 9 | 10 | 2 | |||||||

M4.F3 | 6 | 6 | 2 | |||||||

M5.F4 | 5 | 5 | ||||||||

M6.F4 | 2 | 4 | 4 | 2 |

**Table 4.**Clustering of 684 recordings (from a cluster) re-clustered, 91% score, 2-cluster vs. symmetric conditioned entropy.

0 | 1 | 0 | 1 | 2 | 3 | ||
---|---|---|---|---|---|---|---|

C1 | 43 | 327 | C1 | 44 | 321 | 5 | |

C2 | 314 | C2 | 196 | 106 | 12 |

**Table 5.**Clustering 196 recordings from the highlighted cluster in Table 4 to serial number level.

0 | 1 | 2 | 3 | 4 | |
---|---|---|---|---|---|

M1.F1 | 14 | 1 | |||

M2.F1 | 7 | 7 | |||

M3.F1 | 7 | 7 | |||

M4.F1 | 11 | ||||

M5.F1 | 11 | ||||

M6.F1 | 12 | ||||

M7.F1 | 14 | ||||

M8.F1 | 4 | 10 | 2 | ||

M1.F2 | 12 | 2 | |||

M2.F2 | 12 | ||||

M3.F2 | 14 | ||||

M4.F2 | 1 | 17 | |||

M5.F2 | 2 | 7 | |||

M6.F2 | 7 | 2 | |||

M7.F2 | 3 | 10 |

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**MDPI and ACS Style**

Hofer, E.; v. Mohrenschildt, M.
Model-Free Data Mining of Families of Rotating Machinery. *Appl. Sci.* **2022**, *12*, 3178.
https://doi.org/10.3390/app12063178

**AMA Style**

Hofer E, v. Mohrenschildt M.
Model-Free Data Mining of Families of Rotating Machinery. *Applied Sciences*. 2022; 12(6):3178.
https://doi.org/10.3390/app12063178

**Chicago/Turabian Style**

Hofer, Elizabeth, and Martin v. Mohrenschildt.
2022. "Model-Free Data Mining of Families of Rotating Machinery" *Applied Sciences* 12, no. 6: 3178.
https://doi.org/10.3390/app12063178