70 Chapter 3. Data-Driven Inference of Fault Tree Models Exploiting Symmetry and Modularisation BE4 BE8 AND OR BE5 BE7 BE9 BE10 BE6 BE1 BE3 BE2 OR OR OR AND BE5 BE7 BE9 OR AND S.I. (c) (d) (a) S.I. Subtree found withSymLearn Failure No failure Threshold Control nodes Mirrored subtree OR AND BE6 BE9 BE10 BE4 BE6 BE9 BE5 OR OR AND AND OR BE8 BE5 BE9 BE7 BE5 BE1 BE2 BE2 BE3 BE7 BE9 BE9 BE7 BE9 BE6 BE10 BE10 F F BE1 BE2 BE3 BE6 BE5 BE5 BE4 BE8 BE7 BE9 BE10 (b) AND AND AND OR OR OR BE6 BE6 Figure 3.4: Example case TS1 modelling a symmetric truss bridge system. (a) Model. (b) Depiction of failure/no-failure states. (c) FT inferred by FT-MOEA. (d) FT inferred by SymLearn. Top corresponds to the truss system instability. Generation of Failure Dataset. Based on case TS1 (Figure 3.4) we explain how we use numerical truss system models to generate complete failure datasets. TS1 consists of 10 elements (interpreted as BEs), and two symmetric loads applied on the control nodes. We model damage by reducing close to zero the cross-sectional area of at least one element in the truss system model, and by determining the displacements and stresses in the components due to the applied loads at the nodes of the linear-elastic numerical model. We generate a synthetic failure dataset Dby randomly drawing 106 data points for the status of elements in the truss model via Monte Carlo simulation, and evaluating structural instability (S.I.) based on the displacement of control nodes. Experimental Setup. We compare the SymLearn tool with 3 di!erent back-ends in Step 5, to infer the FT from data. • FT-MOEAis used in 4 di!erent settings: (1) All is the default setting using both modules and symmetries; (2) No Symis All but without symmetries; (3) No rec. is All but without recursive calls for further sub-division; (4) FT-MOEA
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