62 Chapter 3. Data-Driven Inference of Fault Tree Models Exploiting Symmetry and Modularisation analysis of FTs is important for the risk management of complex engineering systems. An important challenge in FTA is the creation of faithful FT models. Therefore, inference of FTs, also known as construction (Salem, Apostolakis, and Okrent, 1976), synthesis (Hunt, Kelly, Mullhi, et al., 1993), or induction (Madden and Nolan, 1994), has been investigated since the 1970s. Three categories of approaches exist: (i) Knowledge-based methods were investigated first, and are semiautomated approaches that derives an FT from a knowledge-based representation using heuristics (Carpignano and Poucet, 1994). These deploy techniques such as decision tables (Salem, Apostolakis, and Okrent, 1976; Wang and Liu, 1993), mini FTs (Powers and Tompkins, 1974; Taylor, 1982), and Piping and Instrumentation Diagrams (Taylor, 1982; Xie, Xue, and Xi, 1993). (ii) Model-based techniques derive an FT by translating a system model (e.g., using AADL (Joshi, Vestal, and Binns, 2007; Mahmud and Mian, 2014), Digraphs (De Vries, 1990; Lapp and Powers, 1977), Simulink (Xiang, Yanoo, Maeno, et al., 2011), or SysML (Mhenni, Nguyen, and Choley, 2014; Xiang, Yanoo, Maeno, et al., 2011)) into an FT. (iii) Due to the increasing availability of inspection and monitoring data, data-driven inference methods have emerged. These automatically infer an FT closely matching a given structured dataset, exploiting techniques like Bayesian networks (Linard, Bueno, Bucur, et al., 2020) and genetic algorithms (Linard, Bucur, and Stoelinga, 2019; Jimenez-Roa, Heskes, Tinga, et al., 2023). The resulting FTs closely match the given dataset but only contain events also present in the data—and therefore may lack rare events. Nevertheless, data-driven inference can provide a good basis for FT creation. A key drawback of data-driven inference methods is that they still lack su"cient scalability for larger systems. In this work, we tackle the scalability challenge of FT inference by exploiting two concepts commonly used in FTs: symmetries and modules. Symmetries between components are commonly present in real-world systems, e.g., due to structural properties or redundancies in safety-critical systems. Modules correspond to subsystems and allow to subdivide the inference problem into smaller, possibly independent, problems. Our approach, called SymLearn, automatically identifies symmetries and modules, and exploits them to reduce the solution space. We implemented the SymLearn method in Python and numerically evaluated it in five case studies, including three truss system models, which are structural systems typically found in civil infrastructures such as roofs, transmission towers, and bridges. We compare SymLearn to the previous FT-MOEA implementation (JimenezRoa, Heskes, Tinga, et al., 2023), which was shown to be faster than its predecessor FT-EA (Linard, Bucur, and Stoelinga, 2019). Our experiments show that: (1) SymLearn is orders of magnitude faster than FT-MOEA if modules and symmetries can be exploited; (2) SymLearn is in some cases slower than inference based on Boolean formulas, it yields, however, more compact FTs than Boolean methods.
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