42 Chapter 2. Automatic Inference of Fault Tree Models via Multi-Objective Evolutionary Algorithms 2.1 Introduction Fault Tree Analysis (FTA) is a widely used method in reliability engineering and risk analysis, mainly because it enables modelling complex systems by encoding and displaying logical relationships that can be used, among others, to understand how a system might fail, trace the root cause of the failure, identify critical components, and calculate the system and subsystem failure probabilities. Fault Tree (FT) models exist since the 1960s and have been used in a wide range of domains, including the automotive, aerospace, and nuclear industries (Kabir, 2017). However, a major drawback of FTs is related to their construction, which is traditionally carried out in conjunction with domain expertise and in a hand-crafted manner, resulting in a tedious and time-consuming task. In the case of complex industrial systems, manual development of these models can lead to incompleteness, inconsistencies, and even errors (Signoret and Leroy, 2021). The above challenge has been discussed since the 1970s, and it is referred to in the literature as construction (Salem, Apostolakis, and Okrent, 1976), synthesis (Hunt, Kelly, Mullhi, et al., 1993), or induction (Madden and Nolan, 1994) of FTs. In this work, we refer to this as automatic inference of FT models, which in general, is the process that automatically (with limited human intervention) produces an FT model given compatible input information. This problem shares some similarities with System Identification (SI), where the objective is to identify the mathematical model of a given system (Johnson and Husbands, 1990), although one di!erence we observe between SI and FTs inference is that for SI it is necessary to pre-define a model structure (e.g., based on laws of physics), which is not possible in the case of FTs inference as this is a task of the inference process itself. Table 2.1: Toy input failure dataset. BE1 BE2 BE3 TE 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 We identify FTs inference challenging because there are many possible FTs for a given failure dataset, and finding the best match is not trivial. Existing methods fail as (i) they need too much human intervention to add assumptions e.g., to deal with complex dependencies between components; (ii) they do not scale adequately in real-world applications, especially algorithms that perform exhaustive search have exponential time complexity; (iii) they result in complex FT structures, (iv) it is unknown how reliable they are under noisy data. We are interested in data-driven approaches, whose challenge is illustrated by the following example: Table 2.1 shows a toy input failure dataset (Section I.4.2). Suppose the associated system is composed of the components BE1, BE2 and BE3, where 0 and 1 are used as non-faulty and faulty states, respectively. TEcorresponds to the system-level failure.
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