76 Chapter 4. Fault Tree inference using Multi-Objective Evolutionary Algorithms and Confusion Matrix-based metrics 4.1 Introduction Fault Tree Analysis (FTA) (NASA, 2002; Ruijters and Stoelinga, 2015) is a critical tool in reliability engineering and risk analysis, utilised extensively in industry for its ability to model complex systems and assess failure probabilities. Despite its creation in the 1960s and widespread application across a large range of industrial domains, the construction of fault trees remains a significant e!ort. Traditional methods involve manual, expert-driven development, a process that is not only laborious but also prone to errors and inconsistencies, especially in complex systems. A promising approach is the automatic inference of Fault Tree (FT) models from failure data. Given a set of data points representing the status of components (operational/failed) and the corresponding overall system status, the aim is to automatically infer a compact FT model capturing the failure behaviour present in the dataset. While first inference approaches date back to the 1970s (Madden and Nolan, 1994), the recent surge of data collection allows new approaches for FT inference (Nauta, Bucur, and Stoelinga, 2018; Waghen and Ouali, 2019; LazarovaMolnar, Niloofar, and Barta, 2020; Jimenez-Roa, Volk, and Stoelinga, 2022). A recent algorithm for creating FT models from failure datasets is FT-MOEA (JimenezRoa, Heskes, Tinga, et al., 2023), which employs both the Elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) (Deb, Pratap, Agarwal, et al., 2002) and the Crowding-Distance (Martí, Segredo, (nchez-Pi, et al., 2017). The former leverages multi-objective optimisation and Pareto front concepts to infer FT models, while the latter serves as a diversity criterion, prioritising diverse solutions over overcrowded ones. However, FT-MOEA encounters challenges related to robustness, scalability, and convergence speed. Robustness pertains to its ability to consistently yield the same results. Scalability refers to the capacity to handle larger FTs, characterised by a greater number of basic events and Minimal Cut Sets (MCSs). Convergence speed concerns e"ciency in completing the task. These problems may stem from the limited features considered in FT-MOEA’s optimisation process. Specifically, FT-MOEA incorporates only three features: error metrics based on accuracy and MCS, and the FT size, with the first two being correlated. Furthermore, computing MCSs for larger FTs is notably computationally expensive, which aggravates scalability and convergence speed concerns. To address these challenges, this chapter explores alternative features to guide the multi-objective optimisation’s convergence process, resulting in the development of the FT-MOEA-CM algorithm. This algorithm leverages 16 metrics derived from the well-established Confusion Matrix (CM) and eliminates the need for the computationally expensive MCS calculations. Our methodology is structured into two phases: In a first phase, we performfeature assessment and identify the most informative and e!ective features for guiding the
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