3 3.4. Experimental evaluation 69 Step 6: Copy Symmetric FTs. After obtaining an FTFM for MCSs M, we obtain the symmetric FTFM→ for the symmetric MCSs M↑ =ϑ(M) by copying FM and replacing each BE b with its symmetric BE ϑ(b). The original and the symmetric FT are then joined under an OR-gate. Example 7 (Copy symmetric FT). We continue with Example 6. Copying the purple sub-tree in Figure 3.1 and applying symmetry ϑ2 =(AE)(CD) yields the symmetric (dark blue) FT. Joining both FTs with an OR-gate yields Module 1. 3.4 Experimental evaluation We implemented the SymLearn methodology in a Python toolchain, available at zenodo.org/record/5571811, and evaluate our approach on five case studies, see Table 3.1: Cases SC and SS are two small systems, depicted in Figure 3.3(c) and running example of Figure 3.1, respectively. Further, we consider three truss system models. N5 N10 N11 N12 N13 N6 N7 N8 N9 N1 N2 N3 N4 BE1 BE5 BE9 BE13 BE17 BE21 BE22 BE23 BE24 BE18 BE19 BE20 BE14 BE15 BE16 BE10 BE11 BE12 BE6 BE7 BE8 BE2 BE3 BE4 F F F (a) Case TS2. N1 N2 N3 N9 N10 N4 N5 N6 N11 N7 N8 BE1 BE10 BE11 BE12 BE13 BE14 BE15 BE16 BE17 BE18 BE20 BE19 BE2 BE3 BE9 BE4 BE5 BE6 BE7 BE8 F (b) Case TS3. A D E F B C (c) Case SC. Figure 3.3: Visualisation of case studies TS2, TS3 and SC. Truss System Cases. Truss systems, commonly used in civil infrastructure like transmission towers, and bridges (see Figure 3.4(a)), are composed of elements connected by nodes, forming rigid bodies under tensile stress. Table 3.1: Overview of case studies. Case #BEs |D| |CD| SC 6 64 4 SS 10 1,024 8 TS1 10 1,024 16 TS2 24 16,777,216 26 TS3 20 1,048,576 18 These systems exhibit a high degree of symmetry and a modular structure. Additionally, they allow for failure datasets to be generated through structural analysis, similar to Byun and Song, 2020. Thus, truss systems provide a highly suitable model for evaluating SymLearn in realistic scenarios. We use three truss system variants: Cases TS1 (Figure 3.4(a)) and TS2 (Figure 3.3(a)) are typical configurations in bridges, while Case TS3 (Figure 3.3(b)) is found in roofs. Note that Case TS1 contains no independent modules, whereas TS2 and TS3 contain four and two modules, respectively.
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