Accurate prediction of the remaining useful life (RUL) of industrial machinery is essential for reducing downtime and optimizing maintenance schedules. Existing approaches, such as long short-term memory (LSTM) networks and convolutional neural networks (CNNs), often struggle to model both global temporal dependencies and fine-grained degradation trends in multivariate sensor data. We propose a hybrid model, FTT-GRU, which combines a Fast Temporal Transformer (FTT) -- a lightweight Transformer variant using linearized attention via fast Fourier transform (FFT) -- with a gated recurrent unit (GRU) layer for sequential modeling. To the best of our knowledge, this is the first application of an FTT with a GRU for RUL prediction on NASA CMAPSS, enabling simultaneous capture of global and local degradation patterns in a compact architecture. On CMAPSS FD001, FTT-GRU attains RMSE 30.76, MAE 18.97, and $R^2=0.45$, with 1.12 ms CPU latency at batch=1. Relative to the best published deep baseline (TCN--Attention), it improves RMSE by 1.16\% and MAE by 4.00\%. Training curves averaged over $k=3$ runs show smooth convergence with narrow 95\% confidence bands, and ablations (GRU-only, FTT-only) support the contribution of both components. These results demonstrate that a compact Transformer-RNN hybrid delivers accurate and efficient RUL predictions on CMAPSS, making it suitable for real-time industrial prognostics.

Data-driven models accurately perform early battery prognosis to prevent equipment failure and further safety hazards. Most existing machine learning (ML) models work in offline mode which must consider their retraining post-deployment every time new data distribution is encountered. Hence, there is a need for an online ML approach where the model can adapt to varying distributions. However, existing online incremental multistep forecasts are a great challenge as there is no way to correct the model of its forecasts at the current instance. Also, these methods need to wait for a considerable amount of time to acquire enough streaming data before retraining. In this study, we propose iFSNet (incremental Fast and Slow learning Network) which is a modified version of FSNet for a single-pass mode (sample-by-sample) to achieve multistep forecasting using pseudo targets. It uses a simple linear regressor of the input sequence to extrapolate pseudo future samples (pseudo targets) and calculate the loss from the rest of the forecast and keep updating the model. The model benefits from the associative memory and adaptive structure mechanisms of FSNet, at the same time the model incrementally improves by using pseudo targets. The proposed model achieved 0.00197 RMSE and 0.00154 MAE on datasets with smooth degradation trajectories while it achieved 0.01588 RMSE and 0.01234 MAE on datasets having irregular degradation trajectories with capacity regeneration spikes.

Introduction As engineering fields mature, new technologies are emerging that are beginning to serve as the foundation of many societal improvements. For example, modern medical diagnostic equipment provides valuable information that gives medical professionals a better understanding of a patient's needs and ultimately improves quality of life [1]. Improvements to vehicle designs make transportation in cars or aircraft safer and more environmentally friendly [2]. Military equipment continues to be developed that better supports and protects personnel in the field [3]. Manufacturing practices and robotic equipment improve work safety conditions and reduce a product's price point, making amenities available to a wider range of consumers [4]. One approach to maximizing system availability is to incorporate some means of health assessment into the system itself. Doing so is often referred to as "integrated system health management" (ISHM) or "prognostics and health management" (PHM), which has been applied successfully to many complex systems [5]. By integrating health assessment into the very functioning of a system, more information can be obtained that provides a better understanding of the system as a whole, thus allowing system owners to become proactive in how they deal with system degradation. ISHM and PHM promise to focus on system conditions, thus supporting initiatives in what has become known as condition-based maintenance (CBM). This, in turn, enables maintenance events to be initiated based on specific system conditions rather than waiting until a failure occurs [6]. One of the key ingredients of ISHM/PHM is diagnostics, which corresponds to the process of determining the health state of the system based on sets of observations (or tests). Such tests are designed specifically to track system behavior and determine whether or not a failure has occurred. In many cases it is impossible to identify a single fault that explains the observations with certainty. Instead, candidate sets of faults are often indicated, and when using applicable models, probabilities or confidence values are associated with the faults to provide additional information. One historic approach to using test observations for diagnosis is to apply a decision tree - sometimes referred to as a fault tree1 [7].

With the rapid advancement of generative artificial intelligence, large language models (LLMs) are increasingly adopted in industrial domains, offering new opportunities for Prognostics and Health Management (PHM), addressing challenges such as high development costs, long deployment cycles, and limited generalizability. However, despite the grow ing synergy between PHM and LLM s, existing evaluation methodologies often fall short regarding structural completeness, dimensional comprehensiveness, and evaluatio n granularity, severely hampering the in - depth integration of LLMs into the PHM domain. To address these limitations, this study, drawing upon two decades of PHM research and recent advancements in LLM - driven PHM systems, proposes PHM - Bench, a novel three - dimensional evaluation framework for PHM - oriented large models. Grounded in the triadic structure of fundamental capabilit y, core task, and entire lifecycle, PHM - Bench is designed specifically for the unique demands of PHM system engineering. It systematically defines multi - level evaluation metrics spanning knowledge comprehension, algorithmi c generation, task optimization, etc., aligning with typical PHM tasks including condition monitoring, fault diagnosis, fault & RUL prediction, and maintenance decision - making, thus establishing a comprehensive assessment mechanism, bridg ing complex engineering systems' design, development, and operational stages. Utilizing both self - constructed case sets and publicly available industrial dataset s, PHM - Bench enables multi - dimensional evaluation of general - purpose and domain - specific models across diverse PHM tasks. Experiments demonstrate its effectiveness in revealing model capabilities and limitations, distinguishing performance across tasks, and providing a unified baseline for model development and optimization. PHM - Bench lays the methodological foundation for industrial - scale assessment of LLMs in PHM and offers a critical benchmark to guide the transition from general - purpose to PHM - specialized models.

The Prognostics and Health Management Data Challenge (PHM) 2016 tracks the health state of components of a semiconductor wafer polishing process. The ultimate goal is to develop an ability to predict the measurement on the wafer surface wear through monitoring the components health state. This translates to cost saving in large scale production. The PHM dataset contains many time series measurements not utilized by traditional physics based approach. On the other hand task, applying a data driven approach such as deep learning to the PHM dataset is non-trivial. The main issue with supervised deep learning is that class label is not available to the PHM dataset. Second, the feature space trained by an unsupervised deep learner is not specifically targeted at the predictive ability or regression. In this work, we propose using the autoencoder based clustering whereby the feature space trained is found to be more suitable for performing regression. This is due to having a more compact distribution of samples respective to their nearest cluster means. We justify our claims by comparing the performance of our proposed method on the PHM dataset with several baselines such as the autoencoder as well as state-of-the-art approaches.

A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive performance. However, in order to optimally plan maintenance operations, it is also important to quantify the uncertainty inherent to the predictions. This issue can be addressed by turning standard frequentist neural networks into Bayesian neural networks, which are naturally capable of providing confidence intervals around the estimates. Several methods exist for training those models. Researchers have focused mostly on parametric variational inference and sampling-based techniques, which notoriously suffer from limited approximation power and large computational burden, respectively. In this work, we use Stein variational gradient descent, a recently proposed algorithm for approximating intractable distributions that overcomes the drawbacks of the aforementioned techniques. In particular, we show through experimental studies on simulated run-to-failure turbofan engine degradation data that Bayesian deep learning models trained via Stein variational gradient descent consistently outperform with respect to convergence speed and predictive performance both the same models trained via parametric variational inference and their frequentist counterparts trained via backpropagation. Furthermore, we propose a method to enhance performance based on the uncertainty information provided by the Bayesian models. We release the source code at https://github.com/lucadellalib/bdl-rul-svgd.

Industrial Cyber-Physical Systems (ICPS) integrate the disciplines of computer science, communication technology, and engineering, and have emerged as integral components of contemporary manufacturing and industries. However, ICPS encounters various challenges in long-term operation, including equipment failures, performance degradation, and security threats. To achieve efficient maintenance and management, prognostics and health management (PHM) finds widespread application in ICPS for critical tasks, including failure prediction, health monitoring, and maintenance decision-making. The emergence of large-scale foundation models (LFMs) like BERT and GPT signifies a significant advancement in AI technology, and ChatGPT stands as a remarkable accomplishment within this research paradigm, harboring potential for General Artificial Intelligence. Considering the ongoing enhancement in data acquisition technology and data processing capability, LFMs are anticipated to assume a crucial role in the PHM domain of ICPS. However, at present, a consensus is lacking regarding the application of LFMs to PHM in ICPS, necessitating systematic reviews and roadmaps to elucidate future directions. To bridge this gap, this paper elucidates the key components and recent advances in the underlying model.A comprehensive examination and comprehension of the latest advances in grand modeling for PHM in ICPS can offer valuable references for decision makers and researchers in the industrial field while facilitating further enhancements in the reliability, availability, and safety of ICPS.

The aim of Predictive Maintenance, within the field of Prognostics and Health Management (PHM), is to identify and anticipate potential issues in the equipment before these become critical. The main challenge to be addressed is to assess the amount of time a piece of equipment will function effectively before it fails, which is known as Remaining Useful Life (RUL). Deep Learning (DL) models, such as Deep Convolutional Neural Networks (DCNN) and Long Short-Term Memory (LSTM) networks, have been widely adopted to address the task, with great success. However, it is well known that this kind of black box models are opaque decision systems, and it may be hard to explain its outputs to stakeholders (experts in the industrial equipment). Due to the large number of parameters that determine the behavior of these complex models, understanding the reasoning behind the predictions is challenging. This work presents a critical and comparative revision on a number of XAI methods applied on time series regression model for PM. The aim is to explore XAI methods within time series regression, which have been less studied than those for time series classification. The model used during the experimentation is a DCNN trained to predict the RUL of an aircraft engine. The methods are reviewed and compared using a set of metrics that quantifies a number of desirable properties that any XAI method should fulfill. The results show that GRAD-CAM is the most robust method, and that the best layer is not the bottom one, as is commonly seen within the context of Image Processing.

The main objective of Prognostics and Health Management is to estimate the Remaining Useful Lifetime (RUL), namely, the time that a system or a piece of equipment is still in working order before starting to function incorrectly. In recent years, numerous machine learning algorithms have been proposed for RUL estimation, mainly focusing on providing more accurate RUL predictions. However, there are many sources of uncertainty in the problem, such as inherent randomness of systems failure, lack of knowledge regarding their future states, and inaccuracy of the underlying predictive models, making it infeasible to predict the RULs precisely. Hence, it is of utmost importance to quantify the uncertainty alongside the RUL predictions. In this work, we investigate the conformal prediction (CP) framework that represents uncertainty by predicting sets of possible values for the target variable (intervals in the case of RUL) instead of making point predictions. Under very mild technical assumptions, CP formally guarantees that the actual value (true RUL) is covered by the predicted set with a degree of certainty that can be prespecified. We study three CP algorithms to conformalize any single-point RUL predictor and turn it into a valid interval predictor. Finally, we conformalize two single-point RUL predictors, deep convolutional neural networks and gradient boosting, and illustrate their performance on the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) data sets.

In fault detection and diagnosis of prognostics and health management (PHM) systems, most of the methodologies utilize machine learning (ML) or deep learning (DL) through which either some features are extracted beforehand (in the case of ML) or filters are used to extract features autonomously (in case of DL) to perform the critical classification task. Particularly in the fault detection and diagnosis of industrial robots where electric current, vibration or acoustic emissions signals are the primary sources of information, a feature domain that can map the signals into their constituent components with compressed information at different levels can reduce the complexities and size of typical ML and DL-based frameworks. The Deep Scattering Spectrum (DSS) is one of the strategies that use the Wavelet Transform (WT) analogy to separate and extract the information encoded in a signal's various temporal and frequency domains. As a result, the focus of this work is on the study of the DSS's relevance to fault detection and daignosis for mechanical components of industrail robots. We used multiple industrial robots and distinct mechanical faults to build an approach for classifying the faults using low-variance features extracted from the input signals. The presented approach was implemented on the practical test benches and demonstrated satisfactory performance in fault detection and diagnosis for simple and complex classification problems with a classification accuracy of 99.7% and 88.1%, respectively.