Accurately forecasting lithium-ion battery capacity degradation is crucial for optimizing the second-life utilization of these batteries, enabling reliable operation, reduced maintenance costs, and extended life cycle performance. However, achieving consistent forecasting accuracy across cells and over time remains challenging due to significant cell-to-cell variability and substantial changes in real-world usage conditions during the transition from first to second life. In this study, we propose a new physics-informed machine learning method that integrates an aging-aware electrochemical model with a recurrent neural network, creating a physics-informed recurrent neural network (PI-RNN). This hybrid model leverages both physics-based insights and data-driven learning to predict capacity fade under diverse usage conditions, including transitions from first- to second-life applications. We evaluate PI-RNN using two datasets: an open-source NASA dataset comprising 28 lithium cobalt oxide/graphite cells, and a newly collected dataset of 39 commercial lithium iron phosphate/graphite cells, where cells were initially cycled to 80% capacity in their first life before undergoing milder cycling in their second life. While PI-RNN performs comparably to data-driven models in the first-life phase, it demonstrates a clear advantage in second-life forecasting, reducing root mean squared error by approximately 40%–70% compared to baseline models when forecasting periods span the transition from first to second life, even when trained on as few as two cells. Parametric studies highlight the advantages of incorporating physics-based modeling, and uncertainty quantification ensures the reliability of long-term capacity forecasting. In addition, we conducted benchmarking studies to systematically assess the advantages and limitations of the proposed model, thus identifying the scenarios where this approach excels.

PrognosticsAircraft Prognostics and Health Management (PHM) is a multidisciplinary framework that provides vital information to operators to ensure maximum system uptime and system safety. It does this by estimating the current and future condition (health) of engineering systems and providing decision support. In recent years, PHM has evolved from being a post hoc maintenance support tool to an essential system that should be integrated throughout all stages of the equipment lifecycle. This chapter describes the essential steps of how PHM can be used in the design and manufacturing of future aircraft. There are many benefits in adopting and evaluating PHM in the design stage. This includes a system that is ultimately easier to monitor and maintain, has better logistics, has reduced overall costs, and has less unplanned downtime. As such, it is argued here that PHM should be designed together with the aircraft. Therefore, this chapter proposes a methodology that includes PHM considerations at all stages of aircraft design. By promoting the integration of these disciplines − PHM, engineering design and manufacturing −, we hope to contribute to more reliable and safe aircraft that can achieve more cost-effective operations and a more sustainable future.

Deep learning has demonstrated significant potential for prognostics in complex systems (Fink et al., 2020). Recent advances in physics-informed machine learning have integrated physics-of-failure principles within data-driven models (Arias Chao, Kulkarni, Goebel, & Fink, 2022). Beyond physical laws, fleet-level time-to-failure (TTF) distributions provide valuable prior knowledge for individual asset life predictions. In this paper we derive a probabilistic analytical health index(HI) model based on power-law degradation, enabling a probabilistic description that reconciles individual variability with fleet-wide trends. We show that, under Weibull, Gamma, and Pareto-distributed TTFs, the HI evolution follows an analytical form, allowing explicit characterization of time to reach intermediate degradation levels. Therefore, this work provides a theoretical foundation for integrating reliability principles with deep learning, advancing towards Reliability-Informed Deep Learning (RIDL). The approach is validated on synthetic turbofan engine data and real-world battery degradation datasets. This work establishes a rigorous basis for embedding reliability engineering principles into deep learning, improving predictive maintenance and remaining useful life (RUL) estimation.

Accurately estimating a Health Index (HI) from condition monitoring data (CM) is essential for reliable and interpretable prognostics and health management (PHM) in complex systems. In most scenarios, complex systems operate under varying operating conditions and can exhibit different fault modes, making unsupervised inference of an HI from CM data a significant challenge. Hybrid models combining prior knowledge about degradation with deep learning models have been proposed to overcome this challenge. However, previously suggested hybrid models for HI estimation usually rely heavily on system-specific information, limiting their transferability to other systems. In this work, we propose an unsupervised hybrid method for HI estimation that integrates general knowledge about degradation into the convolutional autoencoder's model architecture and learning algorithm, enhancing its applicability across various systems. The effectiveness of the proposed method is demonstrated in two case studies from different domains: turbofan engines and lithium batteries. The results show that the proposed method outperforms other competitive alternatives, including residual-based methods, in terms of HI quality and their utility for Remaining Useful Life (RUL) predictions. The case studies also highlight the comparable performance of our proposed method with a supervised model trained with HI labels.

Hybrid models combining physical knowledge and machine learning show promise for obtaining accurate and robust prognostic models. However, despite the increased interest in hybrid models in recent years, the proposed solutions tend to be domain-specific. As a result, there is no compelling strategy of what, where, and how physics-derived knowledge can be integrated into deep learning models depending on the available representation of physical knowledge and the quality of data for the development of prognostic models for complex systems. This Ph.D. project aims to develop a general strategy for hybridizing prognostic models by exploring multiple methods to incorporate physical knowledge at various stages of the learning algorithm. The project will prioritize general expert knowledge as the primary source of information, while domain-specific knowledge will serve as an additional feature when applicable.

Discovering health indicators (HI) is essential for prognostics and health management of complex systems, as an HI enables timely interventions and effective maintenance strategies. However, most of the existing methodologies for HI discovery rely on labeled data which is expensive and complicated to obtain in the real world. In this paper, we propose a novel, unsupervised physics-informed model structured after expert knowledge in the form of a graphical representation of the expected relationships between sensor readings, operating conditions, and degradation. In addition, a soft constraint is used to guide the representation of the HI according to generally available expert knowledge about degradation. We evaluated the model on a turbofan engine dataset and conducted four experiments by manipulating the original data to create realistic real-world scenarios. The proposed method discovers an HI that exhibits better intrinsic qualities than the current state-of-the-art methodologies, leading to enhanced prognostic performance. Notably, in situations where the initial health state of each system varies, the proposed method achieves an average prognostic performance improvement of approximately 20% compared to existing state-of-the-art methods.