Olga Tsurkan, Aleksandra Konstantinova, Aleksandr Sedykh, Dmitrii Zhiganov, Arsenii Senokosov, Daniil Tarpanov, Matvei Anoshin, and Leonid Fedichkin L.D. Landau Dept. of Theoretical Physics, Moscow Institute of Physics and Technology, Institutsky Per. 9, Dolgoprudny, Moscow Region, 141701 Russia (Dated: April 30, 2025) Predictive maintenance in aerospace heavily relies on accurate estimation of the remaining useful life of jet engines. In this paper, we introduce a Hybrid Quantum Recurrent Neural Network framework, combining Quantum Long Short-Term Memory layers with classical dense layers for Remaining Useful Life forecasting on NASA's Commercial Modular Aero-Propulsion System Simulation dataset. Each Quantum Long Short-Term Memory gate replaces conventional linear transformations with Quantum Depth-Infused circuits, allowing the network to learn high-frequency components more effectively. Experimental results demonstrate that, despite having fewer trainable parameters, the Hybrid Quantum Recurrent Neural Network achieves up to a 5% improvement over a Recurrent Neural Network based on stacked Long Short-Term Memory layers in terms of mean root mean squared error and mean absolute error. Moreover, a thorough comparison of our method with established techniques, including Random Forest, Convolutional Neural Network, and Multilayer Perceptron, demonstrates that our approach, which achieves a Root Mean Squared Error of 15.46, surpasses these baselines by approximately 13.68%, 16.21%, and 7.87%, respectively. Nevertheless, it remains outperformed by certain advanced joint architectures. Our findings highlight the potential of hybrid quantum-classical approaches for robust time-series forecasting under limited data conditions, offering new avenues for enhancing reliability in predictive maintenance tasks. Keywords: Remaining Useful Life, Quantum Machine Learning, Recurrent Neural Network, LSTM, Predictive Maintenance, Time-Series Forecasting I. INTRODUCTION Accurate estimation of the remaining useful life (RUL) of critical machinery is a cornerstone of modern reliability and risk-management strategies [1-3].

The accurate prediction of RUL for lithium-ion batteries is crucial for enhancing the reliability and longevity of energy storage systems. Traditional methods for RUL prediction often struggle with issues such as data sparsity, varying battery chemistries, and the inability to capture complex degradation patterns over time. In this study, we propose a survival analysis-based framework combined with deep learning models to predict the RUL of lithium-ion batteries. Specifically, we utilize five advanced models: the Cox-type models (Cox, CoxPH, and CoxTime) and two machine-learning-based models (DeepHit and MTLR). These models address the challenges of accurate RUL estimation by transforming raw time-series battery data into survival data, including key degradation indicators such as voltage, current, and internal resistance. Advanced feature extraction techniques enhance the model's robustness in diverse real-world scenarios, including varying charging conditions and battery chemistries. Our models are tested using 10-fold cross-validation, ensuring generalizability and minimizing overfitting. Experimental results show that our survival-based framework significantly improves RUL prediction accuracy compared to traditional methods, providing a reliable tool for battery management and maintenance optimization. This study contributes to the advancement of predictive maintenance in battery technology, offering valuable insights for both researchers and industry practitioners aiming to enhance the operational lifespan of lithium-ion batteries.

Predicting the remaining useful life (RUL) of ball bearings plays an important role in predictive maintenance. A common definition of the RUL is the time until a bearing is no longer functional, which we denote as an event, and many data-driven methods have been proposed to predict the RUL. However, few studies have addressed the problem of censored data, where this event of interest is not observed, and simply ignoring these observations can lead to an overestimation of the failure risk. In this paper, we propose a probabilistic estimation of RUL using survival analysis that supports censored data. First, we analyze sensor readings from ball bearings in the frequency domain and annotate when a bearing starts to deteriorate by calculating the Kullback-Leibler (KL) divergence between the probability density function (PDF) of the current process and a reference PDF. Second, we train several survival models on the annotated bearing dataset, capable of predicting the RUL over a finite time horizon using the survival function. This function is guaranteed to be strictly monotonically decreasing and is an intuitive estimation of the remaining lifetime. We demonstrate our approach in the XJTU-SY dataset using cross-validation and find that Random Survival Forests consistently outperforms both non-neural networks and neural networks in terms of the mean absolute error (MAE). Our work encourages the inclusion of censored data in predictive maintenance models and highlights the unique advantages that survival analysis offers when it comes to probabilistic RUL estimation and early fault detection.

The prediction of RUL has garnered significant attention from both academic researchers and industry professionals. This is because accurately predicting RUL can significantly enhance the effectiveness of predictive maintenance, leading to increased machine reliability and reduced incidences of failures and associated repair costs. Existing RUL prediction models generally fall within two primary categories: the model-based and data-driven approaches [8]. The model-based approach relies on a certain level of physical knowledge about machine degradation to predict RUL, such as employing theories of the Paris law for bearing defect growth [18] and reliability laws [42, 3, 44]. However, integrating such physical knowledge into models can be challenging, especially concerning complex machinery where such insights might not always be readily available.

A core part of maintenance planning is a monitoring system that provides a good prognosis on health and degradation, often expressed as remaining useful life (RUL). Most of the current data-driven approaches for RUL prediction focus on single-point prediction. These point prediction approaches do not include the probabilistic nature of the failure. The few probabilistic approaches to date either include the aleatoric uncertainty (which originates from the system), or the epistemic uncertainty (which originates from the model parameters), or both simultaneously as a total uncertainty. Here, we propose ensemble neural networks for probabilistic RUL predictions which considers both uncertainties and decouples these two uncertainties. These decoupled uncertainties are vital in knowing and interpreting the confidence of the predictions. This method is tested on NASA's turbofan jet engine CMAPSS data-set. Our results show how these uncertainties can be modeled and how to disentangle the contribution of aleatoric and epistemic uncertainty. Additionally, our approach is evaluated on different metrics and compared against the current state-of-the-art methods.

Lithium-ion batteries are widely used in various applications, including portable electronic devices, electric vehicles, and renewable energy storage systems. Accurately estimating the remaining useful life of these batteries is crucial for ensuring their optimal performance, preventing unexpected failures, and reducing maintenance costs. In this paper, we present a comprehensive review of the existing approaches for estimating the remaining useful life of lithium-ion batteries, including data-driven methods, physics-based models, and hybrid approaches. We also propose a novel approach based on machine learning techniques for accurately predicting the remaining useful life of lithium-ion batteries. Our approach utilizes various battery performance parameters, including voltage, current, and temperature, to train a predictive model that can accurately estimate the remaining useful life of the battery. We evaluate the performance of our approach on a dataset of lithium-ion battery cycles and compare it with other state-of-the-art methods. The results demonstrate the effectiveness of our proposed approach in accurately estimating the remaining useful life of lithium-ion batteries.

Value iteration can find the optimal replenishment policy for a perishable inventory problem, but is computationally demanding due to the large state spaces that are required to represent the age profile of stock. The parallel processing capabilities of modern GPUs can reduce the wall time required to run value iteration by updating many states simultaneously. The adoption of GPU-accelerated approaches has been limited in operational research relative to other fields like machine learning, in which new software frameworks have made GPU programming widely accessible. We used the Python library JAX to implement value iteration and simulators of the underlying Markov decision processes in a high-level API, and relied on this library's function transformations and compiler to efficiently utilize GPU hardware. Our method can extend use of value iteration to settings that were previously considered infeasible or impractical. We demonstrate this on example scenarios from three recent studies which include problems with over 16 million states and additional problem features, such as substitution between products, that increase computational complexity. We compare the performance of the optimal replenishment policies to heuristic policies, fitted using simulation optimization in JAX which allowed the parallel evaluation of multiple candidate policy parameters on thousands of simulated years. The heuristic policies gave a maximum optimality gap of 2.49%. Our general approach may be applicable to a wide range of problems in operational research that would benefit from large-scale parallel computation on consumer-grade GPU hardware.

Modern industries require efficient and reliable machinery. To ensure the stability of industrial equipment and avoid unnecessary downtime, it is important to gauge a machine's remaining useful life (RUL) accurately. This has been done using deep learning-based approaches. In particular, deep neural networks are considered promising in this regard. These include recurrent neural networks (RNNs), convolutional neural networks (CNNs), or hybrid networks.

A major problem of structural health monitoring (SHM) has been the prognosis of damage and the definition of the remaining useful life of a structure. Both tasks depend on many parameters, many of which are often uncertain. Many models have been developed for the aforementioned tasks but they have been either deterministic or stochastic with the ability to take into account only a restricted amount of past states of the structure. In the current work, a generative model is proposed in order to make predictions about the damage evolution of structures. The model is able to perform in a population-based SHM (PBSHM) framework, to take into account many past states of the damaged structure, to incorporate uncertainties in the modelling process and to generate potential damage evolution outcomes according to data acquired from a structure. The algorithm is tested on a simulated damage evolution example and the results reveal that it is able to provide quite confident predictions about the remaining useful life of structures within a population.

This paper presents the data-driven techniques and methodologies used to predict the remaining useful life (RUL) of a fleet of aircraft engines that can suffer failures of diverse nature. The solution presented is based on two Deep Convolutional Neural Networks (DCNN) stacked in two levels. The first DCNN is used to extract a low-dimensional feature vector using the normalized raw data as input. The second DCNN ingests a list of vectors taken from the former DCNN and estimates the RUL. Model selection was carried out by means of Bayesian optimization using a repeated random subsampling validation approach. The proposed methodology was ranked in the third place of the 2021 PHM Conference Data Challenge.