72 Chapter 3. Data-Driven Inference of Fault Tree Models Exploiting Symmetry and Modularisation encodes all the MCSs. In contrast, the other configurations using FT-MOEA did not always yield a completely accurate FT (i.e., ωc, ωd >0.0), for example, case TS1. The error stems from the multi-objective optimisation which also aims to provide a small FT and the evolutionary algorithm which can fall into local optima. However, for the cases TS2 and TS3 (with independent modules), all configurations of SymLearn (All, No Sym, No rec.) outperformed FT-MOEA by returning an FT that accurately reflects the input (ωc =ωd =0.0). This shows the clear benefit of subdividing the problem using independent modules. Figure 3.5(c) shows the advantage of using FT-MOEA as a back-end compared to Boolean logic, since the sizes of the returned FTs can be considerably smaller. The FTs inferred using Espresso or Sympy can be twice as large as the ones resulting fromFT-MOEA. The reason is that for the Boolean logic formulas, no simplifications were performed by the libraries and the resulting FTs are therefore exactly encoding all the MCSs. Notice that the original FT-MOEA yields smaller or equal FT sizes than any of the configurations of SymLearn. This smaller size can however also come at the cost of losing accuracy, as demonstrated by case TS2. The larger FTs in SymLearn mostly stem from the composition of partitions where shared BE occur in both sub-trees, see for example Figure 3.4(c) and 3.4(d). While explicitly capturing the symmetries can therefore increase the size of the resulting FT, it also provides more insights into the system. Figure 3.5(d) shows that SymLearn (All) runs significantly faster than FT-MOEA alone. If independent modules are present (cases TS2, TS3, SC and SS), SymLearn yields an FT within at most 2minwhile FT-MOEArequires at least 1h. The benefit of exploiting symmetries and modules can also be seen when comparing configuration All to No Sym and No. rec. which both run longer. Note that for SymLearn nearly all computation time is spent in the FT-MOEA back-end (Step 5). Computing the modules and symmetries (Steps 2-4) took 50milliseconds at most whereas the computation of the MCSs (Step 1) took 43seconds at most (for case TS2). Configurations based on Boolean functions always yield a result within minutes, but yield significantly larger FTs. 3.5 Conclusions We presented SymLearn, a data-driven algorithm that infers a Fault Tree (FT) model from given failure data in a fully automatic way by identifying and exploiting modules and symmetries. Our evaluation based on truss system models shows that SymLearn is significantly faster than only using evolutionary algorithms when modules and symmetries can be exploited. In the future, we aim to further improve the scalability by optimising the inference process. First, the current partitioning of the Minimal Cut Sets requires the top gate to be an OR-gate. We aim to support the AND-gate as well. In addition, the
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