# Metaheuristics and Support Vector Data Description for Fault Detection in Industrial Processes

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Support Vector Data Description

#### 2.2. Spotted Hyena Optimizer (SHO)

#### 2.2.1. Encircling Prey

#### 2.2.2. Hunting

#### 2.2.3. Attacking the Prey

#### 2.2.4. Searching for Prey (Exploration)

#### 2.3. Krill Herd Algorithm (KH)

- (i)
- movement generated by other krill;
- (ii)
- food search activity;
- (iii)
- physical diffusion.

#### 2.4. Squirrel Search Algorithm SSA

#### 2.5. Particle Swarm Optimization

## 3. Methodology for Fault Detection

## 4. Industrial Application

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Description | |
---|---|

$x{f}_{1}$ | [${\mathrm{F}}^{\circ}$], Nozzle 1 |

$x{f}_{2}$ | [${\mathrm{F}}^{\circ}$], Nozzle 2 |

$x{f}_{3}$ | [Percent], Heating power zone 1 |

$x{f}_{4}$ | [Percent], Heating power zone 2 |

$x{f}_{5}$ | [Percent], Heating power zone 3 |

$x{f}_{6}$ | [Percent], Heating power zone 4 |

$x{f}_{7}$ | [Percent], Heating power zone 5 |

$x{f}_{8}$ | [Percent], Heating power zone 6 |

$x{f}_{9}$ | [in], Mold position value |

$x{f}_{10}$ | [in], Opening run |

$x{f}_{11}$ | [US ton], Closing force peak value |

$x{f}_{12}$ | [US ton], Closing force real value |

$x{f}_{13}$ | [s], Mold protection time |

$x{f}_{14}$ | [${\mathrm{F}}^{\circ}$], Oil temperature |

$x{f}_{15}$ | [${\mathrm{F}}^{\circ}$], Traverse |

$x{f}_{16}$ | [s], Cooling time |

$x{f}_{17}$ | [psi], Backpressure |

$x{f}_{18}$ | [${\mathrm{in}}^{3}$], Volume end screw |

holding pressure | |

$x{f}_{19}$ | [psi], Holding pressure |

$x{f}_{20}$ | [${\mathrm{in}}^{3}$/s], Dosage power |

$x{f}_{21}$ | [psi], Pressure at Switchover |

$x{f}_{22}$ | [s], Cycle time |

$x{f}_{23}$ | [lbf-ft], Mean spin |

$x{f}_{24}$ | [lbf-ft], Peak value at spin |

$x{f}_{25}$ | [psi], Specific injection pressure |

$x{f}_{26}$ | [${\mathrm{in}}^{3}$], Dosage volume |

$x{f}_{27}$ | [${\mathrm{in}}^{3}$], Injection volume |

$x{f}_{28}$ | [s], Dosing time |

$x{f}_{29}$ | [s], Injection time |

$x{f}_{30}$ | [${\mathrm{F}}^{\circ}$], Cylinder zone 1 |

$x{f}_{31}$ | [${\mathrm{F}}^{\circ}$], Cylinder zone 2 |

$x{f}_{32}$ | [${\mathrm{F}}^{\circ}$], Cylinder zone 3 |

$x{f}_{33}$ | [${\mathrm{F}}^{\circ}$], Cylinder zone 4 |

$x{f}_{34}$ | [ft/s], Revolutions |

$x{f}_{35}$ | [Wh], Injection work |

$x{f}_{36}$ | [${\mathrm{in}}^{3}$], Switching volume |

SHO | KH | SSA | PSO | |
---|---|---|---|---|

Number of iterations | 200 | 200 | 200 | 200 |

Population size | 50 | 50 | 50 | 50 |

${v}_{f}=0.02$, | ${N}_{fs}=3$ | $w=0.5$ | ||

Other parameters | ${D}^{max}=0.005$, | ${c}_{1}={c}_{2}=2$, | ||

${N}^{max}=0.01$ | ||||

${w}_{n}=0.1+0.8(1-i/200)$ |

F1 Score | Time | |||||||
---|---|---|---|---|---|---|---|---|

SHO | KH | SSA | PSO | SHO | KH | SSA | PSO | |

1 | 0.9620 | 0.9189 | 0.9610 | 0.9189 | 76.6396 | 112.7972 | 139.2550 | 207.6410 |

2 | 0.9744 | 0.9189 | 0.9189 | 0.9189 | 78.2157 | 114.3666 | 149.3458 | 209.0972 |

3 | 0.9512 | 0.9189 | 0.9750 | 0.9189 | 77.4362 | 113.8831 | 129.8195 | 208.6143 |

4 | 0.9744 | 0.9189 | 0.9189 | 0.9189 | 77.4033 | 113.4381 | 149.1254 | 208.5458 |

5 | 0.9744 | 0.9189 | 0.9189 | 0.9189 | 77.6753 | 114.3179 | 147.2649 | 207.9583 |

6 | 0.9750 | 0.9189 | 0.9189 | 0.9189 | 76.9510 | 113.6539 | 155.0708 | 209.6714 |

7 | 0.9744 | 0.9189 | 0.9744 | 0.9189 | 77.3957 | 114.0773 | 142.7828 | 211.6702 |

8 | 0.9750 | 0.9189 | 0.9750 | 0.9333 | 79.0279 | 113.6960 | 128.8649 | 212.5049 |

9 | 0.9750 | 0.9189 | 0.9189 | 0.9189 | 78.7634 | 113.6895 | 143.1924 | 208.9668 |

10 | 0.9744 | 0.9189 | 0.9211 | 0.9189 | 83.3741 | 113.5960 | 142.3234 | 209.6382 |

11 | 0.9630 | 0.9189 | 0.9750 | 0.9189 | 80.4753 | 113.8772 | 116.8845 | 210.7641 |

12 | 0.9750 | 0.9189 | 0.9189 | 0.9189 | 82.3348 | 114.1014 | 151.0041 | 209.1223 |

13 | 0.9750 | 0.9189 | 0.9189 | 0.9189 | 79.5617 | 114.0026 | 149.3981 | 208.3499 |

14 | 0.9750 | 0.9189 | 0.9189 | 0.9189 | 78.9463 | 114.1080 | 146.5968 | 208.5490 |

15 | 0.9750 | 0.9189 | 0.9189 | 0.9189 | 79.7457 | 113.7620 | 151.1163 | 210.4518 |

16 | 0.9744 | 0.9189 | 0.9351 | 0.9189 | 88.0263 | 113.7218 | 135.8897 | 209.4198 |

17 | 0.9512 | 0.9189 | 0.9189 | 0.9189 | 78.0516 | 113.8042 | 147.1367 | 209.8243 |

18 | 0.9620 | 0.9189 | 0.9189 | 0.9189 | 77.6847 | 113.7368 | 147.1347 | 213.8261 |

19 | 0.9744 | 0.9744 | 0.9189 | 0.9189 | 77.9648 | 98.1384 | 145.6228 | 208.7176 |

20 | 0.9620 | 0.9744 | 0.9189 | 0.9189 | 79.1865 | 114.2702 | 152.3700 | 208.1235 |

21 | 0.9744 | 0.9744 | 0.9189 | 0.9189 | 79.1609 | 114.2038 | 146.7939 | 209.6390 |

22 | 0.9750 | 0.9744 | 0.9189 | 0.9189 | 76.4243 | 114.1394 | 148.8082 | 210.0689 |

23 | 0.9630 | 0.9744 | 0.9189 | 0.9189 | 76.2201 | 113.5049 | 147.7095 | 207.0849 |

24 | 0.9750 | 0.9744 | 0.9189 | 0.9189 | 78.9390 | 113.6086 | 145.8267 | 208.5851 |

25 | 0.9750 | 0.9744 | 0.9189 | 0.9189 | 75.2608 | 113.7726 | 149.5031 | 225.5017 |

26 | 0.9744 | 0.9744 | 0.9744 | 0.9189 | 74.3404 | 113.8676 | 129.5610 | 210.0427 |

27 | 0.9744 | 0.9744 | 0.9189 | 0.9189 | 74.6434 | 114.3396 | 148.6370 | 207.7600 |

28 | 0.9620 | 0.9744 | 0.9750 | 0.9189 | 74.9797 | 113.4536 | 131.1206 | 209.6813 |

29 | 0.9620 | 0.9750 | 0.9189 | 0.9189 | 74.6099 | 93.0891 | 154.4285 | 207.8903 |

30 | 0.9750 | 0.9750 | 0.9189 | 0.9189 | 76.3885 | 114.4280 | 157.7352 | 213.1721 |

Mean | 0.9702 | 0.9411 | 0.9321 | 0.9194 | 78.1942 | 112.6482 | 144.3441 | 210.0294 |

Std | 0.0074 | 0.0277 | 0.0232 | 0.0026 | 2.8170 | 4.6904 | 9.1777 | 3.3325 |

Source | SS | df | MS | Chi-sq | p-Value |
---|---|---|---|---|---|

Columns | 56,089.6 | 3 | 18,696.5 | 57.3 | 2.2188 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-12}$ |

Error | 60,398.9 | 116 | 520.7 | ||

Total | 116,488.5 | 119 |

Source | SS | df | MS | Chi-sq | p-Value |
---|---|---|---|---|---|

Columns | 135,000 | 3 | 45,000 | 111.57 | 5.0394 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-24}$ |

Error | 8990 | 116 | 77.5 | ||

Total | 143,990 | 119 |

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**MDPI and ACS Style**

Navarro-Acosta, J.A.; García-Calvillo, I.D.; Avalos-Gaytán, V.; Reséndiz-Flores, E.O. Metaheuristics and Support Vector Data Description for Fault Detection in Industrial Processes. *Appl. Sci.* **2020**, *10*, 9145.
https://doi.org/10.3390/app10249145

**AMA Style**

Navarro-Acosta JA, García-Calvillo ID, Avalos-Gaytán V, Reséndiz-Flores EO. Metaheuristics and Support Vector Data Description for Fault Detection in Industrial Processes. *Applied Sciences*. 2020; 10(24):9145.
https://doi.org/10.3390/app10249145

**Chicago/Turabian Style**

Navarro-Acosta, Jesús Alejandro, Irma D. García-Calvillo, Vanesa Avalos-Gaytán, and Edgar O. Reséndiz-Flores. 2020. "Metaheuristics and Support Vector Data Description for Fault Detection in Industrial Processes" *Applied Sciences* 10, no. 24: 9145.
https://doi.org/10.3390/app10249145