66 Chapter 3. Data-Driven Inference of Fault Tree Models Exploiting Symmetry and Modularisation Algorithm 1 Identifying independent modules M1, . . . , Mn from the MCSs CD. Input: MCSs CD. Output: Partitioning M1, . . . , Mn of CD, corresponds to independent modules M1, . . . , Mn. Partitioning ′{{C} | C↓CD} while ∞M, M↑ ↓Partitioning with Mand M↑ sharing BE do Partitioning ′(Partitioning\{M, M↑}) ∝{M∝M↑} return Partitioning ={M1, . . . , Mn}, modules-M1 =BEsM1, . . . , Mn =BEsMn. Step 2: Identify Independent Modules. Our aim is to partition the MCSs CDs.t. an FT for each partition can be learned individually. This allows for a more e"cient inference which could even be performed in parallel. We start by trying to find independent modules fromCDas described in Algorithm 1. The initial partitioning uses each cut set of CDas its own partition. If two partitions share BE, they must be merged to satisfy the constraint for independent modules in Definition 4. We iteratively merge partitions until their BEs are disjoint. The BEs then form the independent modules. The following Steps 3-5 are performed for each independent module and corresponding MCSs individually. The FTs created for the modules are combined by an OR-gate in the end. Example 3 (Identify independent modules). We use the MCSs CD={{A, C}, {B, C}, {B, D}, {D, E}, {F, H}, {G, H}, {G, I}, {I, K}} corresponding to Figure 3.1. Applying the algorithm, cut sets {A, C} and {B, C}, for instance, are merged as they share BE C. In the end, the independent modules and partitioning are: M1 ={A, B, C, D, E} M1 : {{A, C}{B, C}, {B, D}, {D, E}} M2 ={F, G, H, I, K} M2 : {{F, H}{G, H}, {G, I}, {I, K}} Extraction of BE. As an additional optimisation, we automatically derive BE which occur in all minimal cut sets of a partition. In order for the partition to cause a system failure, all these BE must fail. Hence, they are excluded from all MCSs and the approach continues on the reduced MCS. In the end, the excluded BE are joined under an AND-gate with the FT resulting from the reduced MCSs. Step 3: Identify Symmetries. Next, we identify the symmetries ZCD fromCD in a fully automated manner. The simplest way is a brute-force approach trying out all possible permutations and checking whether they are valid symmetries according to Definition 5. While this approach is factorial in |BEs|, we obtain good performance in practice by exploiting two optimisations.
RkJQdWJsaXNoZXIy MjY0ODMw