PSI - Issue 57

Olivier Vo Van et al. / Procedia Structural Integrity 57 (2024) 104–111 O. VoVan / Fatigue Design 2023 00 (2023) 000–000

108

5

Line number

Average temperature damage Number of squat / km

515000 655000

6.43 8.16

1.87 2.20

Table 1: Selection of two line sharing the same properties. These two lines group approximately the same number of rail segments.

significant temperature damage as well. The Table 1 showcases a chosen pair of two lines that are comparable in terms of operational factors such as tonnage, train speed, and curvature. It illustrates that despite sharing many properties, the average temperature-induced damage across segments is associated with a higher occurrence of defects per kilometre.

Fig. 2: Histogram of cyclic loadings computed by Rainflow algo rithm.

Fig. 3: Evolution of damage against day considering variations during the day(blue) or not (green).

3.2. Analysis of variable importance sensitivity

Learning data. The results of this study consider the en tire French rail network as a set of rail segments of 100 meters length. The service tracks are excluded from the study and rail lines (left and right) are considered sepa rately. We consider approximately 800,000 segments, each characterized by the following attributes: the total tonnage of tra ffi c on the line, the tonnage specific to freight, the ton nage specific to passengers, the linear mass of the steel, the rail cant (the inclination between the two rails, particularly on curves), acceleration and deceleration rates, and the 3rd quartile of the speed distribution (representing the speed value at which only a quarter of the trains exceeded). Ton nages are measured in tonnes per year and computed using 6 years of data, rail cant is measured in millimetres, and the speed distribution is based on measurements taken over a month (specifically, February 2020).

Fig. 4: Map of annual evolution of rail damage by daily tempera ture variation.

Learning and implementation details. In the learning phases, the cross-validation is performed on homogeneous sets of assets so that two rail segments of the same line are in the same group (or Fold ), thus avoiding overfitting phenomena. The algorithm used is a Random Forest implemented in the scikit-learn [19] library with the following parameter : the number of trees is set to 192 and the minimum number of samples in leaf nodes, which plays the role of regularization is 250. Regarding the implementations, the default MDI criterion used is the one implemented in scikit-learn [19]. The permutation-based importance is implemented by referring to the documentation provided by