Prognostics and Health Management (PHM) is critical for predicting the Remaining Useful Life (RUL) of systems, a key enabler of Predictive Maintenance (PdM). This paper reviews state-of-the-art data-driven prognostic models, emphasizing four essential characteristics: uncertainty, robustness, interpretability, and feasibility. While traditional research has focused on enhancing RUL prediction accuracy, this review argues that these additional characteristics are equally vital for addressing the demands of PHM applications. The review examines Machine Learning (ML) techniques, stochastic models, and Bayesian filters (BFs), analyzing their strengths, limitations, and trade-offs. ML models excel in accuracy but often lack robust uncertainty quantification and adaptability across varying operational conditions. Stochastic models demonstrate greater robustness and feasibility, performing reliably with limited or variable data. Bayesian filters provide high interpretability and do not require run-to-failure data but face challenges in adapting to diverse environments. To bridge these gaps, this paper proposes a structured Model Evaluation Framework that integrates users’ specific needs with key model characteristics identified in the review. By quantifying the importance of the four characteristics, the framework enables systematic evaluation and selection of prognostic models. The findings underscore the need for advancements in uncertainty quantification, adaptive methods to improve robustness, and enhanced interpretability to meet practical and regulatory requirements. While current models offer valuable insights, further improvements are necessary to unlock their full potential for PHM and PdM applications, ensuring more reliable and actionable predictions.

Prognostics and health management (PHM) in aviation systems aim to predict remaining useful life (RUL), enhancing reliability, while considering operational uncertainties. Hidden Markov Models (HMMs) model degradation processes when damage states are unobservable, using representative features from condition monitoring (CM) data. Traditional HMMs struggle with geometric decay in hidden state durations, leading to the introduction of hidden semi-Markov models (HSMMs), albeit with increased computational complexity. This study compares HMMs and HSMMs, while introducing a dynamic prognostic expression. Using NASA's C-MAPSS dataset, encompassing diverse flight conditions and simulated engine failures, we validate the superiority of HSMMs over HMMs. Moreover, our novel time-dependent prognostic expression outperforms standard ones, highlighting its effectiveness in RUL prognosis.

Prognostics and health management (PHM) is becoming increasingly important as engineering structures and systems grow more complex. Many of these systems lack accurate physical models to describe their degradation, especially in unpredictable scenarios. To meet safety regulations, robust prognostic models are needed to transform sensor data into reliable predictions about a system’s remaining useful life (RUL). This study presents the adaptive hidden semi-Markov model (AHSMM), a novel probabilistic approach that enhances RUL prediction accuracy, uncertainty quantification (UQ), and reliability assessment compared to a long short-term memory (LSTM) model. A key contribution is an in-house experimental campaign involving glass fiber-reinforced polymer specimens subjected to fatigue loading and multiple impact events at different locations and time intervals. Unlike traditional models that rely on data from similar damage histories, the AHSMM is trained exclusively on unimpacted specimens and tested on multiply impacted ones, showcasing its adaptability to previously unseen conditions. The study also introduces a new prognostic performance measure tailored to AHSMM and develops a conditional reliability analysis for both AHSMM and LSTM predictions. Results demonstrate that AHSMM consistently outperforms LSTM across all evaluation metrics. It achieves a 24% lower RMSE over the full lifetime and superior UQ, with an average coverage of 0.79 compared to 0.17 for LSTM. Conditional reliability analysis further shows that AHSMM provides more accurate and stable reliability estimates as data accumulates. By capturing the degradation process and adapting to evolving conditions, AHSMM strengthens prognostic robustness. This study highlights the need for robust PHM models that can handle real-world uncertainties and contribute to advancements in the aerospace, automotive, and defense industries.

The identification of the Purkinje conduction system in the heart is a challenging task, yet essential for a correct definition of cardiac digital twins for precision cardiology. Here, we propose a probabilistic approach for identifying the Purkinje network from non-invasive clinical data such as the standard electrocardiogram (ECG). We use cardiac imaging to build an anatomically accurate model of the ventricles; we algorithmically generate a rule-based Purkinje network tailored to the anatomy; we simulate physiological electrocardiograms with a fast model; we identify the geometrical and electrical parameters of the Purkinje-ECG model with Bayesian optimization and approximate Bayesian computation. The proposed approach is inherently probabilistic and generates a population of plausible Purkinje networks, all fitting the ECG within a given tolerance. In this way, we can estimate the uncertainty of the parameters, thus providing reliable predictions. We test our methodology in physiological and pathological scenarios, showing that we are able to accurately recover the ECG with our model. We propagate the uncertainty in the Purkinje network parameters in a simulation of conduction system pacing therapy. Our methodology is a step forward in creation of digital twins from non-invasive data in precision medicine. An open source implementation can be found at http://github.com/fsahli/purkinje-learning.