8 Chapter 1. Introduction 1.2.3 Markov Process-based Prognostics Prognostics: An overview Prognostics—from the Greek prognostikos—is the cornerstone concept enabling predictability in PHM (Stage 4 in Figure 1.2). Within an engineering context, the science of prognostics attempts to answer: how long will it be until a particular future event or state is reached? (Goebel, Celaya, Sankararaman, et al., 2017). Therefore, the main aim of prognostics is to predict an event or state before its occurrence, making time a critical variable (Lee, F. Wu, Zhao, et al., 2014). Among the most popular outcomes of prognostics is the estimation of the Remaining Useful Life (RUL), which measures the time until failure. However, estimating the time to reach alternative states to failure may be relevant for some applications, as discussed later in this section. This capability makes prognostics key within the PHM paradigm, enabling taking actions before failures occur, thus allowing better planning while minimising reactive costs and downtime (Elattar, Elminir, and Riad, 2016). Engineering applications of prognostics are vast, including rotating machinery (Heng, S. Zhang, Tan, et al., 2009); Li-ion batteries (J. Zhang and Lee, 2011); gas turbines (Tahan, Tsoutsanis, Muhammad, et al., 2017); manufacturing (T. Xia, Dong, Xiao, et al., 2018); aircraft (Che, H. Wang, Fu, et al., 2019); and wind turbines (Rezamand, Kordestani, Carriveau, et al., 2020). Prognostic models operate at both system and component levels (S. Kim, Choi, and N. H. Kim, 2021) and come in various types; however, the literature lacks consensus regarding their classifications (Mrugalska, 2019). Therefore, in this dissertation, we discuss the following categories: physics-based, data-driven, and hybrid. For completeness, the literature also mentions knowledge-based prognostics, though they are significantly less prevalent. Thus, we do not discuss them here. For more information, see Sikorska, Hodkiewicz, and Ma, 2011; J. Peng, G. Xia, Y. Li, et al., 2022; Xue, J. Yang, M. Yang, et al., 2023. Physics-based prognostics—also referred to as model-based (Zio, 2022; Xue, J. Yang, M. Yang, et al., 2023)—use explicit mathematical representations to formalise physical failure modes and degradation phenomena. This requires a deep understanding of the system’s physics, operating conditions, and life cycle loads (Elattar, Elminir, and Riad, 2016; Javed, Gouriveau, and Zerhouni, 2017; T. Xia, Dong, Xiao, et al., 2018). The process generally involves model identification, simulations under loads, tracking degradation measures, and predicting RUL (Cubillo, Perinpanayagam, and Esperon-Miguez, 2016). These models are tailored to specific applications, such as crack growth, spall progression, and wear, relying on accurate parameterisation using laboratory or real-time data (Rezamand, Kordestani, Carriveau, et al., 2020; D. An, N. H. Kim, and Choi, 2015). Challenges in physics-based prognostics stem from the complexity
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