PSI - Issue 38

Emilien Baroux et al. / Procedia Structural Integrity 38 (2022) 497–506 E. Baroux et al. / Structural Integrity Procedia 00 (2021) 1– ??

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Fig. 3. Pseudo-damage dispersion over I 11 clients

This multidimensional description of client pseudo-damages helps us to compare clients on each component of the vector. In the next paragraph, we will apply variable reduction methods to achieve a simpler and su ffi cient description of client pseudo-damage vectors towards their statistical distribution.

3.4. Driving profile description

We perform a principal component analysis (PCA) to describe the variations of pseudo-damage vectors using fewer dimensions (Husson et al. (2011)). The principal components (PC) (or principal axes) are linear combinations of the pseudo-damages with maximum variance and are pairwise orthogonal. Here, the first three components express 97.9% of data variability, see Table 1. The Table 1 also shows the correlation of each PC to the pseudo-damage’s components. First component PC1 is positively correlated to all pseudo-damages. This is called the size e ff ect: a client with a high (resp. low) coordinate on the PC1 axis has high (resp. low) pseudo-damages overall. The second component PC2 is positively correlated with the pseudo-damages induced from combinations of longitudinal and lateral loads, and negatively correlated with the vertical ones. The third component PC3 is positively correlated with the longitudinal pseudo-damages and negatively with the lateral ones.

Table 1. Principal component analysis: pseudo-damages correlations with the PCs. ˆ D ( F 0 X ) ˆ D ( F 90 X ) ˆ D ( F 0 Y ) ˆ D ( F 90 Y ) ˆ D ( F 0 Z )

ˆ D ( F 90 9.20 -3.70 -0.50

Z )

Corr PC 1 (76.6%) 9.30 Corr PC 2 (13.8%) 2.20

7.80 4.00 4.80

8.50 3.70 -3.70

8.30 4.20 -3.60

9.10 -3.80 -0.20

Corr PC 3 (7.6%)

2.80

A client clusterization (Husson et al. (2011)) reveals five clusters. The projection of the clusters on each PC allows us to describe them (see Fig. 4). The center (0 , 0) of the cloud corresponds to mean pseudo-damage behaviors. PC1 makes it possible to distinguish the clients according to their multiaxial pseudo-damages. The cluster 1 includes clients with significantly lower than mean pseudo-damages. The cluster 2 includes clients C4 and C6 having medium pseudo-damages. The remaining clusters singularize clients C3, C5 and C9. We have explored the question of client damage description. As mentioned in the introduction, we want to question the choice of design loads from statistics on client loads. In the next section, we will discuss the reconstruction of one or a group of these clients from reference proving grounds to further feed this discussion.