1 1.2. Main concepts 9 of the physical failure modes and degradation phenomena, which may not be fully understood, dynamic, and highly non-linear, making their modelling di"cult (Zio, 2022). Data-driven prognostics have gained prominence in the PHM community with the rise of big data and industrial Internet of Things technologies (Xue, J. Yang, M. Yang, et al., 2023), owing to their low cost and ease of deployment, particularly when understanding of physics is limited (Elattar, Elminir, and Riad, 2016; Javed, Gouriveau, and Zerhouni, 2017; Guo, Z. Li, and M. Li, 2020; Heng, S. Zhang, Tan, et al., 2009). These methods extract degradation patterns from historical and condition monitoring data to predict future degradation or state behaviour (Tsui, N. Chen, Q. Zhou, et al., 2015; T. Xia, Dong, Xiao, et al., 2018; Zio, 2022). The literature distinguish mainly two sub-classes of data-driven prognostics: Statistical models and Machine Learning models (Heng, S. Zhang, Tan, et al., 2009; D. An, N. H. Kim, and Choi, 2015; Elattar, Elminir, and Riad, 2016; Tahan, Tsoutsanis, Muhammad, et al., 2017; T. Xia, Dong, Xiao, et al., 2018; Guo, Z. Li, and M. Li, 2020). Statistical—also referred to as Stochastic (Prakash, Yuan, Hazra, et al., 2021)—models include Markov chains, Gaussian process regression, Gamma process, and Bayesian networks. Machine Learning (ML) models—also referred to as Artificial Intelligence (AI) techniques (Javed, Gouriveau, and Zerhouni, 2017)—include neural networks, support vector machines, and fuzzy logic, among others. As an observation, the distinction between statistical and ML models may be ambiguous, and a more thorough discussion around this classification is needed. The shortcomings of data-driven prognostics include the dependency on the availability of extensive, multivariate data covering all operational phases and conditions of the system (Elattar, Elminir, and Riad, 2016; Zio, 2022), which is challenging in some cases, especially in safety-critical systems. Additionally, these types of models may be considered grey- or black-box models (e.g., neural networks) (Xue, J. Yang, M. Yang, et al., 2023), making interpretability di"cult. Hybrid-based prognostics—also known as blended (Xue, J. Yang, M. Yang, et al., 2023) or fusion (Elattar, Elminir, and Riad, 2016)—combine the strengths of physics-based and data-driven approaches to address their weaknesses. Javed, Gouriveau, and Zerhouni, 2017 identifies two types: series and parallel. In series, a physics-based model is updated with new data using an online parameter estimation technique. In parallel, a data-driven model predicts the residuals not explained by the first model. T. Xia, Dong, Xiao, et al., 2018 further classify hybrid prognostics into physics-based + data-driven and data-driven + data-driven. As an example, Rezamand, Kordestani, Carriveau, et al., 2020 provide a detailed analysis of the use of hybrid prognostics for wind turbine components. To date, hybrid-based prognostics receives increased attention as integrated solutions can lead to better problem-solving (Xue, J. Yang, M. Yang, et al., 2023).
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