# Pantograph Sliding Strips Failure—Reliability Assessment and Damage Reduction Method Based on Decision Tree Model

^{*}

## Abstract

**:**

## 1. Introduction

- Control reviews (every 2–4 days);
- Periodic reviews (once a month);
- Large reviews (every 250,000 km ± 10%);
- Smaller repair (every 500,000 km);
- Bigger repair (every 1,000,000 km);
- Major repair (after the course of 4,000,000 km).

## 2. Materials and Methods

#### 2.1. Damage of Pantograph Sliding Strips

- −
- The weight content of metal in carbon material in the 3 kV DC traction power system is <40%;
- −
- The chemical composition (according to the UIC 608: 2003 standard) is C = 75–77%; CU = 12–15%; Pb = 7–10%; Sb = 1–2%

#### 2.2. Machine Learning Method for Failure Prediction of the Pantograph Sliding Strips

#### 2.3. Data Preparation for the Machine Learning

_{1}—replacement of the sliding strip due to the even wear of sliders;

_{2}—replacement of the sliding strip due to the detachment of a fragment of the sliding strip, material extraction or the burning of the sliding strip;

_{3}—replacement of the sliding strip due to the uneven wear of the sliders;

#### 2.4. Development of the Prediction Model

_{1}÷ x

_{10}represent the input data used in the presented model:

- −
- x
_{1}—the review number; - −
- x
_{2}—the identification of the new measure cycle; - −
- x
_{3}—the number of days since the last replacement; - −
- x
_{4}—the quarter of the year; - −
- x
_{5}—the type of the pantograph; - −
- x
_{6}—pantograph location (front, rear); - −
- x
_{7}—the difference in thickness of the sliding strip N_{1}between technical review; - −
- x
_{8}—the difference in thickness of the sliding strip N_{2}between technical review; - −
- x
_{9}—the preview technical state; - −
- x
_{10}—the replacement reason.

_{i}values. The decision tree was built recursively. The root nodes were splatted recursively left and right until the maximum depth was reached. Each step in a prediction involves checking the value of one predictor (variable x

_{1}÷ x

_{10}) and calculating the Gini diversity index. In the proposed model, the maximum number of splits was 100; the Gini diversity index was applied as a split criterion, and there was no surrogate decision split. The Gini diversity index calculates the probability of a specific feature being incorrectly classified when randomly selected. If all the elements are linked to a single class, then it can be called pure. The Gini diversity index varies between values of 0 and 1, where 0 expresses the purity of classification, i.e., all the elements belong to a specified class or only one class exists there. Additionally, 1 indicates the random distribution of elements across various classes. In MATLAB software (MATLAB 2020b, MathWorks, Natick, MA, USA) it is possible to automatically generate the decision tree based on input data and determine the split criterion as well as the number of splits.

## 3. Results

#### 3.1. Reliability Assessment of the Selected Types of Pantographs

_{(f)}= max (Figure 6). This will be the basis for the further failure analysis and supervised machine learning.

**Figure 6.**Weibull probability plots for the selected types of pantograph: (

**a**) DSA-150; (

**b**) AKP-4E; and (

**c**) 5-ZL.

_{f}= max) at which the probability of a given type of pantograph failure is greatest. Additionally, based on the probability density function, a mean time to failure may be calculated as follows:

_{f}= max are presented in Table 4.

#### 3.2. Complex Tree Errors Analysis

_{1}÷ x

_{10}.

#### 3.3. Failure Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Damages of the edge of the carbon sliding strip: (

**a**) minor surface damages; and (

**b**) major surface damages.

**Figure 2.**Wear of the sliding: (

**a**) material melting as a result of arcing; (

**b**) detachment of a piece of carbon strip; (

**c**) crack of a strip; and (

**d**) the top layer of a strip is peeling off [30].

**Figure 3.**Method of three-valued prediction of technical condition based on machine learning and failure analysis for the reference variant—step 1.

**Figure 4.**Method of three-valued prediction of technical condition based on machine learning and failure analysis for variant I—step II.

**Figure 7.**Probability density function for the selected types of pantograph: (

**a**) DSA-150 (red); (

**b**) AKP-4E (black); and (

**c**) 5-ZL (blue).

**Table 1.**Technical data of carbon sliding strips for different sample manufacturers [29].

Manufacturer | Type | Properties | ||||
---|---|---|---|---|---|---|

No. | Resistance | Density | Hardness | Flexural Strength | ||

(µohm) | (g/cm^{3}) | (HRB) | (N/mm^{2}) | |||

1 | Morganite | MY7A2 | 5 | 2.40 | - | 85 |

2 | PanTrac GmbH | RH83M6 | 7 | 3.40 | 105 | 102 |

3 | Elektrokarbon a.s. | SK181 | - | 2.20 | 90 | - |

4 | Mersen (France) | P5696 | 7 | 2.30 | 90 | 85 |

5 | Required value | - | Max 5 | Max 2.50 | Max 120 | Min 65 |

Description | Symbol |
---|---|

Review number | $i$ |

A new measuring cycle | $Cnew$ |

The number of days since the replacement | D |

The quarter of the year | $Q$ |

Current collector type | Top |

Front/rear current collector | $Cc$ |

Difference in the N_{1} thickness between reviews | $Th1$ |

Difference in the N_{2} thickness between reviews | $Th2$ |

Earlier technical condition | $S$ |

The reason for the replacement | $N$ |

Parameters of Weibull Distribution | DSA-150 | AKP-4E | 5-ZL |
---|---|---|---|

β | 1.470337 | 1.153632 | 1.329664 |

η (days) | 74.619087 | 119.655763 | 134.032580 |

Type of Pantograph | MTTF (Day) | t_{f} = max (Day) |
---|---|---|

DSA-150 | 67.53 | 35 |

AKP-4 | 113.77 | 21 |

5-ZL | 123.25 | 48 |

The Number of Predicted Technical Conditions | Technical Condition | |||
---|---|---|---|---|

All | 1 | 2 | 3 | |

Correctly classified technical conditions (%) | 84.62 | 89.16 | 52.08 | 97.92 |

Incorrectly classified technical conditions (%) | 15.38 | 10.84 | 47.92 | 2.08 |

Predicted cases (%) | 84.62 | 88.29 | 53.19 | 100.00 |

Unpredicted cases (%) | 15.38 | 11.70 | 46.81 | 0.00 |

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**MDPI and ACS Style**

Kuźnar, M.; Lorenc, A.; Kaczor, G.
Pantograph Sliding Strips Failure—Reliability Assessment and Damage Reduction Method Based on Decision Tree Model. *Materials* **2021**, *14*, 5743.
https://doi.org/10.3390/ma14195743

**AMA Style**

Kuźnar M, Lorenc A, Kaczor G.
Pantograph Sliding Strips Failure—Reliability Assessment and Damage Reduction Method Based on Decision Tree Model. *Materials*. 2021; 14(19):5743.
https://doi.org/10.3390/ma14195743

**Chicago/Turabian Style**

Kuźnar, Małgorzata, Augustyn Lorenc, and Grzegorz Kaczor.
2021. "Pantograph Sliding Strips Failure—Reliability Assessment and Damage Reduction Method Based on Decision Tree Model" *Materials* 14, no. 19: 5743.
https://doi.org/10.3390/ma14195743