# A Decision-Making Tool Based on Exploratory Visualization for the Automotive Industry

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## Abstract

**:**

## 1. Introduction

## 2. Hybrid Unsupervised Exploratory Plots

#### 2.1. Classical Multidimensional Scaling

- Euclidean;
- Squared Euclidean;
- Standardized Euclidean (seuclidean): each coordinate difference between observations is scaled by dividing by the corresponding element of the standard deviation;
- Cityblock;
- Minkowski;
- Chebyshev: maximum coordinate difference;
- Cosine: one minus the cosine of the included angle between points;
- Correlation: one minus the sample correlation between points;
- Hamming, which is the percentage of coordinates that differ;
- Jaccard: one minus the Jaccard coefficient, which is the percentage of non-zero coordinates that differ;
- Spearman: one minus the sample Spearman’s rank correlation between observations.

#### 2.2. Sammon Mapping

^{2}).

_{i}, i = 1, ..., N. It is sought to map these into d-dimensional space (with d < L), to obtain vectors Y

_{i}, i = 1, ... N; d

_{ij}is the pairwise distance between Y

_{i}and Y

_{j}, and d

_{ij}

^{*}is the distance between X

_{i}and X

_{j.}

#### 2.3. Factor Analysis (FA)

## 3. A Real Case Study: Waterjet Cutting

- Intensifier: the waterjet pumps or intensifiers [51], which supply water at extremely high pressure to waterjet machines;
- Cyclone: the vacuum cyclone unit located in a waterjet machine, used for suctioning the waste generated towards a chute. It also holds the pieces during the cut.

#### 3.1. Intensifier

- Water leaks: the intensifier will stop working if there is a severe water leak. This is a critical failure with high associated costs, as it stops production;
- High temperature in a cylinder: if high temperature lasts a long time, it could lead to a break in the header;
- Detected SH malfunction; this means that it is necessary to repair the SH, or otherwise it will crash and stop the production. This malfunction/problem is perceived by the maintenance staff.

#### 3.2. Cyclone

- The suction circuit is blocked: the waste absorbing system does not work properly. This is a critical failure as it stops production;
- Vacuum malfunctioning: the vacuum does not work properly. It is an infrequent failure that does not stop production, but could lead to defective parts.

## 4. Results

- PCA: Number of output dimensions—2/3;
- MLHL: Number of output dimensions—2/3; number of iterations—1000/2000/3000; learning rate—0.01/0.005/0.001; p—0.1/0.5;
- CMLHL: Number of output dimensions—2/3; number of iterations—1000/2000/3000; learning rate—0.01/0.005/0.001; p—0.1/0.5; τ—0.05;
- CMDS: Number of output dimensions—2/3; distance metrics—Euclidean/Squared Euclidean/Standardized Euclidean/Cityblock/Minkowski/Chebyshev/Cosine/Correlation/Jaccard/Spearman;
- SM: Number of output dimensions—2/3; number of iterations—100/200/500;
- FA: Number of output dimensions—2/3; 200 iterations maximum;
- k-means: Distances—Squared Euclidean/Cityblock/Cosine/Correlation; k—3/4/6/8;
- Agglomerative clustering: Distances—Euclidean/Chebyshev/Minkowski/Correlation/Seuclidean/Squared Euclidean/Cityblock/Mahalanobis/Cosine/Spearman/Hamming/Jaccard; linkages—average/centroid/complete/median/single/ward/weighted; a cutoff value adjusted to obtain the same number of clusters as in the case of k-means (3/4/6/8).

#### 4.1. Intensifiers Results

- x (red x): water leak;
- + (black +): high temperature in cylinder #1;
- * (cyan *): high temperature in cylinder #2;
- o (green o): detected SH malfunctioning;
**·**(blue point): no problem reported (i.e., intensifier properly working).

**.**These simple visualizations (the right-straight outputs of the EPP methods) are shown for comparison purposes, in order to contrast them with the obtained HUEP visualizations (see below).

#### 4.2. Cyclone Results

- x (red x): suction circuit is blocked;
- + (black +): vacuum malfunctioning;
**·**(blue point): no problem reported (i.e., cyclone properly working).

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANN | Artificial Neural Networks |

CMDS | Classical Multidimensional Scaling |

CMLHL | Cooperative Maximum-Likelihood Hebbian Learning |

EPP | Exploratory Projection Pursuit |

FA | Factor Analysis |

FD | Failure Detection |

HP | Hydraulic Piston |

HUEP | Hybrid Unsupervised Exploratory Plot |

IoT | Internet of Things |

KNN | k-Nearest Neighbour |

MDS | Multidimensional scaling |

ML | Machine Learning |

MLHL | Maximum-Likelihood Hebbian Learning |

PCA | Principal Component Analysis |

PdM | Predictive Maintenance |

SH | Seal Head |

SM | Sammon Mapping |

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**Figure 2.**Example of intensifier and sketch of sensors (blue and red circles). (

**a**) Picture of the intensifier. (

**b**) Sensors placement sketch.

**Figure 3.**Example of a waterjet machine with the cyclone and sketch of sensors (red and green circles). (

**a**) Waterjet machine. (

**b**) Sensors placement sketch.

**Figure 4.**3D visualizations generated by EPP methods for the intensifier dataset. (

**a**) CMLH 3D visualization. (

**b**) FA 3D visualization.

**Figure 5.**HUEP visualizations of the intensifier dataset. EPP+hierarchical clustering. (

**a**) HUEP: PCA+hierarchical clustering (k = 6, Cityblock, and complete). (

**b**) HUEP: MLHL+hierarchical clustering (k = 6, Cityblock, and complete). (

**c**) HUEP: CMLHL+hierarchical clustering (k = 6, Cityblock, and complete). (

**d**) HUEP: CMDS–cityblock+hierarchical clustering (k = 6, Cityblock, and complete). (

**e**) HUEP: SM+hierarchical clustering (k = 6, Cityblock, and complete). (

**f**) HUEP: FA+hierarchical clustering (k = 6, Cityblock, and complete).

**Figure 6.**HUEP visualizations generated by CMDS–Cityblock and different clustering parameters of the intensifier dataset. (

**a**) HUEP: CMDS–Cityblock+k-means (k = 3 and Cityblock). (

**b**) HUEP: CMDS–Cityblock+k-means (k = 6 and Cityblock). (

**c**) HUEP: CMDS–Cityblock+hierarchical clustering (k = 4, Minkowski, and weighted). (

**d**) HUEP: CMDS–Cityblock+hierarchical clustering (k = 6, Chebyshev, and complete). (

**e**) HUEP: CMDS–Cityblock+hierarchical clustering (k = 6, Cityblock, and complete).

**Figure 7.**3D visualizations generated by EPP methods for the cyclone dataset. (

**a**) CMLHL 3D visualization. (

**b**) CMDS–Seuclidean 3D visualization.

**Figure 8.**HUEP visualizations of the cyclone dataset. EPP+hierarchical. (

**a**) HUEP: PCA+hierarchical clustering (k = 6, Cityblock, and weighted). (

**b**) HUEP: MLHL+hierarchical clustering (k = 6, Cityblock, and weighted). (

**c**) HUEP: CMLHL+hierarchical clustering (k = 6, Cityblock, and weighted). (

**d**) HUEP: CMDS–Seuclidean+hierarchical clustering (k = 6, Cityblock, and weighted). (

**e**) HUEP: SM+hierarchical clustering (k = 6, Cityblock, and weighted). (

**f**) HUEP: FA+hierarchical clustering (k = 6, Cityblock, and weighted).

**Figure 9.**HUEP visualizations generated by CMDS–Seuclidean and different clustering parameters for the cyclone dataset. (

**a**) HUEP: CMDS–Seuclidean+k-means (k = 3 and Correlation). (

**b**) HUEP: CMDS–Seuclidean+k-means (k = 6 and Correlation). (

**c**) HUEP: CMDS–Seuclidean+hierarchical clustering (k = 6, Cityblock, and weighted).

**Table 1.**Intensifier features. Variables gathered from each cylinder, SH and HP. XX in the feature name refers to the number of each sensor.

Feature Name | Description | Unit |
---|---|---|

HPXXTemp_oC_avg | HP average temperature | °C |

HPXXTemp_oC_max | HP maximum temperature | °C |

HPXXTemp_oC_min | HP minimum temperature | °C |

HPXXTemp_oC_std | HP standard deviation temperature | °C |

SHXXTemp_oC_avg | SH average temperature | °C |

SHXXTemp_oC_max | SH maximum temperature | °C |

SHXXTemp_oC_min | SH minimum temperature | °C |

SHXXTemp_oC_std | SH standard deviation temperature | °C |

SHXXLeak_mLm | SH increase leak of water since last period | 1.5 mL/increase |

Feature Name | Description | Unit |
---|---|---|

AccPeak_g_avg | Engine vibration average | G |

AccPeak_g_max | Engine vibration maximum | G |

AccPeak_g_min | Engine vibration minimum | G |

AccPeak_g_std | Engine vibration standard deviation | G |

CmdDutyEngineSpeed_Hz | Fan RPM setpoint | Hz |

CmdRestEngineSpeed_percent | % RPM idle setpoint | % |

CmdVacuumPressure_mBar | Vacuum pressure setpoint | mBar |

EngineTemp_oC_avg | Engine temperature average | °C |

EngineTemp_oC_max | Engine temperature maximum | °C |

EngineTemp_oC_min | Engine temperature minimum | °C |

EngineTemp_oC_std | Engine temperature standard deviation | °C |

FanSpeed_Hz_avg | Fan speed average | Hz |

FanSpeed_Hz_max | Fan speed maximum | Hz |

FanSpeed_Hz_min | Fan speed minimum | Hz |

FanSpeed_Hz_std | Fan speed standard deviation | Hz |

VacuumPressure1_mBar_avg | Vacuum pressure sensor1 average | mBar |

VacuumPressure1_mBar_max | Vacuum pressure sensor1 maximum | mBar |

VacuumPressure1_mBar_min | Vacuum pressure sensor1 minimum | mBar |

VacuumPressure1_mBar_std | Vacuum pressure sensor1 standard deviation | mBar |

VacuumPressure2_mBar_avg | Vacuum pressure sensor2 average | mBar |

VacuumPressure2_mBar_max | Vacuum pressure sensor2 maximum | mBar |

VacuumPressure2_mBar_min | Vacuum pressure sensor2 minimum | mBar |

VacuumPressure2_mBar_std | Vacuum pressure sensor2 standard deviation | mBar |

Duration | Cycle time for part production | ms |

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## Share and Cite

**MDPI and ACS Style**

Redondo, R.; Herrero, Á.; Corchado, E.; Sedano, J.
A Decision-Making Tool Based on Exploratory Visualization for the Automotive Industry. *Appl. Sci.* **2020**, *10*, 4355.
https://doi.org/10.3390/app10124355

**AMA Style**

Redondo R, Herrero Á, Corchado E, Sedano J.
A Decision-Making Tool Based on Exploratory Visualization for the Automotive Industry. *Applied Sciences*. 2020; 10(12):4355.
https://doi.org/10.3390/app10124355

**Chicago/Turabian Style**

Redondo, Raquel, Álvaro Herrero, Emilio Corchado, and Javier Sedano.
2020. "A Decision-Making Tool Based on Exploratory Visualization for the Automotive Industry" *Applied Sciences* 10, no. 12: 4355.
https://doi.org/10.3390/app10124355