# Model Selection and Quality Estimation of Time Series Models for Artificial Technical Surface Generation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The ARMAsel-Approach

## 3. Applying the ARMAsel Algorithm for the Description of Rough Surfaces

#### 3.1. Lapped Surfaces (A1–A3)

#### 3.2. Reamed Surfaces (A4–A6)

#### 3.3. Ground Surfaces (B1–B6)

#### 3.4. Horizontally Milled Surfaces (C1–C6)

#### 3.5. Milled Surfaces (D1–D6)

#### 3.6. Turned Surfaces (F1–F6)

## 4. Model Evaluation

## 5. Training of Classifiers with Simulated Data

#### 5.1. Training Data Generation

#### 5.2. CNN Architecture, Traning, and Weights Discussion

^{(nlayers−1)}= 16). The combination of convolution, ReLU layer and pooling is expected to preserve important information while reducing the overall data volume, resulting in a reduction of computation time [38]. The filter sizes are 10 × 1, the number of filters is 32 in the 2nd and 64 in the 3rd layer. The idea behind the constant filter sizes, in combination with the pooling layer is to see local features on the first layer of the CNN and more global features on the third layer of the CNN. The 16 × 125 feature vector is mapped to a 1024 × 1 fully connected layer, which is followed by a dropout layer with 20% dropout probability. The dropout layer is introduced with the idea to prevent overfitting in the model [39]. A visualization of the architecture is given in Figure 9. After the dropout-layer, a SoftMax layer is introduced for classification, which maps the output of the dropout layer to the range [0, 1].

#### 5.3. Classification Performance

#### 5.3.1. Classification Performance with the Full Set of Training Data

#### 5.3.2. Classification Performance with Reduced Set of Training Data

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. ARMAsel Results for Horizontally Milled, Milled and Turned Surfaces

## References

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**Figure 1.**Illustration of the concept: Few measurement data is used for model generation, which in turn is being used for the generation of larger sets of training data. This training data is then applied to a convolutional neuronal network (CNN) for manufacturing process classification.

**Figure 2.**Examined samples of varying manufacturing principles: Six different processes with three and six roughness degrees are considered.

**Figure 7.**PSD comparison of stochastic (Grinding B6) and deterministic (Turning E6) profiles, the PSD-functions of all 50 evaluation areas are displayed.

**Figure 8.**Examples for generated profiles for stochastic (Grinding B6) and deterministic (Turning E6) surfaces.

**Figure 10.**Prediction significance of the CNN trained with the full set of training data A1–E6: Positive values display the difference to the 2nd largest significance of the SoftMax layer. Negative values display the difference from the largest SoftMax significance level to the level of the true class.

**Figure 11.**Prediction significance of the CNN trained with a reduced set of training data: Positive values display the difference to the 2nd largest significance of the SoftMax layer. Negative values display the difference from the largest SoftMax significance level to the level of the true class.

1 (Fine) | 2 | 3 | 4 | 5 | 6 (Rough) | |
---|---|---|---|---|---|---|

Lapping A1–A3 | 793.43 ± 145.66 | 442.52 ± 126.41 | 241.82 ± 92.57 | - | - | - |

Reaming A4–A6 | - | - | - | 125.79 ± 54.51 | 252.67 ± 186.56 | 450.03 ± 241.73 |

Grinding B1–B6 | 599.20 ± 168.52 | 449.88 ± 130.49 | 190.59 ± 81.91 | 107.40 ± 40.61 | 120.47 ± 75.34 | 254.55 ± 167.72 |

Horizontal Milling C1–C6 | 128.49 ± 53.65 | 119.42 ± 65.36 | 633.30 ± 308.22 | 845.03 ± 386.99 | 2365.10 ± 799.30 | 1375.94 ± 539.69 |

Milling D1–D6 | 118.06 ± 38.05 | 176.06 ± 98.03 | 317.77 ± 212.99 | 756.30 ± 398.38 | 1455.34 ± 479.92 | 2335.25 ± 688.24 |

Turning E1–E6 | 126.57 ± 44.75 | 132.47 ± 73.99 | 192.15 ± 127.93 | 1287.04 ± 418.82 | 1864.56 ± 522.53 | 2594.69 ± 802.70 |

**Table 2.**Classification performance of the CNN trained with the full training set A1–E6 with actual measurement data after 2000 training steps (upper row) and 20,000 steps (lower row).

Lapping as | Reaming as | Grinding as | Horizontal Milling as | Milling as | Turning as | |
---|---|---|---|---|---|---|

Lapping in % (n) | 100 (150) | 0 (0) | 27.33 (82) | 0 (0) | 0 (0) | 0 (0) |

98.67 (148) | 0 (0) | 1.33 (4) | 0 (0) | 0 (0) | 0 (0) | |

Reaming in % (n) | 0 (0) | 24 (36) | 0 (0) | 14.67 (44) | 5 (15) | 0 (0) |

0 (0) | 51.33 (77) | 0 (0) | 14 (42) | 3.66 (11) | 0 (0) | |

Grinding in % (n) | 0 (0) | 0.66 (1) | 61.67 (185) | 50 (16,67) | 6.67 (20) | 0 (0) |

1.33 (2) | 0.66 (1) | 96 (288) | 7.33 (22) | 8.67 (26) | 0 (0) | |

Horizontal Milling in % (n) | 0 (0) | 16.67 (25) | 3.67 (11) | 68.33 (205) | 2.67 (8) | 0 (0) |

0 (0) | 16.67 (25) | 1.67 (5) | 76.33 (229) | 13 (39) | 0 (0) | |

Milling in % (n) | 0 (0) | 58.67 (88) | 7.33 (22) | 0.33 (1) | 58.67 (176) | 0 (0) |

0 (0) | 28.67 (43) | 1 (3) | 2.33 (7) | 43.33 (130) | 0 (0) | |

Turning in % (n) | 0 (0) | 0 (0) | 0 (0) | 0 (0) | 27 (81) | 100 (300) |

0 (0) | 2.67 (4) | 0 (0) | 0 (0) | 31.33 (94) | 100 (300) |

**Table 3.**Classification performance of the CNN trained with the reduced training set with actual measurement data after 2000 training steps (upper row) and 20,000 steps (lower row).

Lapping as | Reaming as | Grinding as | Horizontal Milling as | Milling as | Turning as | |
---|---|---|---|---|---|---|

Lapping in % (n) | 100 (150) | 0 (0) | 46 (138) | 8.33 (25) | 0 (0) | 0 (0) |

100 (150) | 0 (0) | 40.33 (121) | 0 (0) | 0 (0) | 0 (0) | |

Reaming in % (n) | 0 (0) | 66.67 (100) | 0 (0) | 16.67 (50) | 18 (54) | 0 (0) |

0 (0) | 83.33 (125) | 16.33 (49) | 16.67 (50) | 50 (150) | 0 (0) | |

Grinding in % (n) | 0 (0) | 33.33 (50) | 54 (162) | 8.33 (25) | 32 (96) | 33.33 (100) |

0 (0) | 14 (21) | 43.33 (130) | 16.67 (50) | 0 (0) | 33.33 (50) | |

Horizontal Milling in % (n) | 0 (0) | 0 (0) | 0 (0) | 66.67 (200) | 16 (48) | 8 (24) |

0 (0) | 2.67 (4) | 0 (0) | 66.67 (200) | 11.33 (34) | 16.67 (50) | |

Milling in % (n) | 0 (0) | 0 (0) | 0 (0) | 0 (0) | 17.33 (52) | 0 (0) |

0 (0) | 0 (0) | 0 (0) | 0 (0) | 12 (36) | 0 (0) | |

Turning in % (n) | 0 (0) | 0 (0) | 0 (0) | 0 (0) | 16.67 (50) | 58.67 (176) |

0 (0) | 0 (0) | 0 (0) | 0 (0) | 26.67 (80) | 50 (150) |

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**MDPI and ACS Style**

Eifler, M.; Ströer, F.; Rief, S.; Seewig, J.
Model Selection and Quality Estimation of Time Series Models for Artificial Technical Surface Generation. *Technologies* **2018**, *6*, 3.
https://doi.org/10.3390/technologies6010003

**AMA Style**

Eifler M, Ströer F, Rief S, Seewig J.
Model Selection and Quality Estimation of Time Series Models for Artificial Technical Surface Generation. *Technologies*. 2018; 6(1):3.
https://doi.org/10.3390/technologies6010003

**Chicago/Turabian Style**

Eifler, Matthias, Felix Ströer, Sebastian Rief, and Jörg Seewig.
2018. "Model Selection and Quality Estimation of Time Series Models for Artificial Technical Surface Generation" *Technologies* 6, no. 1: 3.
https://doi.org/10.3390/technologies6010003