78 Chapter 4. Fault Tree inference using Multi-Objective Evolutionary Algorithms and Confusion Matrix-based metrics Failure dataset {D,N} N Parallelisation Caching + Parallelisation Compute confusion matrix metrics S3 S2 Apply genetic operators FT-MOEA Conv. criteria S5 Apply NSGA-II S4 Parent FTs S1 True False FTD Figure 4.1: FT-MOEA-CM methodology. Blue boxes indicate novel steps. TP and TN correspond to both the FT and the data giving the same result, i.e., fFD(bk) =f D(bk). FP and FN indicate that the outcome of the FT di!ers from the data, i.e., fFD(bk) ⇑ =f D(bk). To assess the FT’s performance relative to input data D, we utilise 17 metrics outlined in Table 4.1. The first metric evaluates the FT’s size via the number of nodes FD, the remaining 16 metrics are derived from the CM. We normalise all CM-based metrics to the interval [0,1] such that 0 represents optimal values. Metrics ranging from→1 to 1, such as the Matthews Correlation Coe!cient are scaled to the interval [0,2] to enhance the interpretability of simulation outcomes. Further details on the CM and associated metrics can be found in Bo)i$, Runje, Lisjak, et al., 2023. 4.3 FT-MOEA-CM’s methodology Figure 4.1 illustrates FT-MOEA-CM’s FT inference process, which utilises multiobjective evolutionary algorithms and metrics derived from the confusion matrix. The approach is based on the standard steps of genetic algorithms: each generation of FTs is mutated based on operators such as adding or removing gates. The resulting FTs are evaluated based on metrics and the best FTs are then used in the next generation. As FT-MOEA-CM is based on FT-MOEA, we direct the reader to Jimenez-Roa, Heskes, Tinga, et al., 2023 for detailed information on the methodology . Below, we outline each main step of the process. (1) - Input: The input includes the failure dataset D(Section 4.2) as well as FT-MOEA-CM’s parameters, such as the maximum population size N. - Process: The initial population consists of two parent FTs, one a single AND-gate and the other an OR-gate, each connecting to all BEs in D. - Output: The parent FTs constitute the FT population. (2) - Input: The existing FT population. - Process: Seven genetic operators (e.g., adding or removing gates, crossover of sub-trees) are applied to alter the structure for each FT in the population
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