RUL Estimation

Estimating remaining shelf life (RSL) from images could provide affordable decision support for perishable produce, but evaluation protocols can substantially affect reported performance when repeated images are available from the same biological specimen. We use the Hass Avocado Ripening dataset, comprising 8,834 image-RSL pairs from 426 fruits across three storage regimes, to evaluate a frozen ImageNet-pretrained visual backbone with a lightweight regression head. Our contributions are threefold: we quantify the effect of observation-level versus specimen-disjoint evaluation, compare lightweight and heavier visual backbones under specimen-disjoint cross-validation, and examine their spatial attributions using Grad-CAM. Across ten observation-level random splits, the model achieves a mean RMSE of 2.37 days with a standard deviation of 0.03 days, whereas specimen-disjoint 5-fold cross-validation yields a mean RMSE of 3.12 days with a standard deviation of 0.11 days. The corresponding mean coefficient of determination is 0.553. A matched per-specimen comparison confirms higher error under specimen-disjoint evaluation, with a probability value below 0.001 across 426 specimens, showing that observation-level partitioning gives a substantially more optimistic estimate for this dataset and model configuration. Under specimen-disjoint evaluation, MobileNetV3-Small (0.93 million parameters) achieves accuracy comparable to ResNet-18 while providing substantially higher throughput, and Grad-CAM reveals differences in spatial attribution between the lightweight backbones. These results support specimen-disjoint evaluation and attribution analysis when assessing lightweight vision models for longitudinal shelf-life prediction.

Predictive maintenance requires reliable remaining useful life (RUL) estimation. Existing methods mainly follow two paradigms: wear-based aging models that capture cumulative degradation and sensor-driven data models that reflect instantaneous health conditions, each providing only partial information. In this work, we propose a probabilistic fusion framework that integrates wear-based and sensor-based prognostic components through failure probability distributions. Based on explicit structural assumptions linking wear, latent health, sensor observations, and failure, we derive a principled combination rule that enables uncertainty-aware integration with adaptive weighting of the components. Experimentally, we assess this combination rule by learning the wear-based component using a parametric survival model and the sensor-based component using a 1D convolutional neural network (1D-CNN) with a post-hoc uncertainty model. Evaluation on multiple N-CMAPSS datasets demonstrates that the fused model improves point accuracy, preserves the C-index, and produces narrower yet well-calibrated prediction intervals compared to either component alone. The results highlight the complementary roles of wear-based survival model and sensor-based deep learning model, and show that their probabilistic integration provides a structured pathway toward more robust and consistent prognostics over the life-time.

In predictive maintenance, early and late RUL prediction errors carry asymmetric consequences, yet hyperparameter optimization typically targets a single accuracy metric that treats both directions equally. This study treats the optimization objective itself as a design variable. Five architectures (MLP, LSTM, XGBoost, TCN, and Transformer) are evaluated under three regimes: single-objective maximization of $R^2$, single-objective minimization of the NASA scoring function, and a multi-objective formulation that jointly optimizes both criteria. The multi-objective search employs NSGA-II with Entropy-CRITIC weighting for Pareto selection. Seventy-five model-dataset-strategy combinations are assessed on the NASA C-MAPSS turbofan and BackBlaze hard-disk drive benchmarks. On C-MAPSS, all strategies achieve comparable accuracy ($R^2 \approx 0.89$), yet multi-objective optimization reduces directional imbalance by approximately 33%, improving calibration of early versus late predictions. Model rankings prove configuration-dependent, with simpler architectures frequently outperforming deeper temporal models. On BackBlaze, the objectives shift from complementary to conflicting, producing divergent Entropy-CRITIC weights and a substantial generalization gap (best $R^2 \approx 0.34$). These results demonstrate that the optimization objective materially shapes prognostic behavior and that multi-objective search provides a practical mechanism for calibrating prediction timeliness in RUL modeling.

Digital twins increasingly support downstream analytical tasks that depend on time-series data, motivating interest in time-series foundation models (TSFMs) as scalable backbones. However, TSFMs are primarily pretrained for temporal continuation and often underperform on unseen tasks such as regression, and systematic empirical comparisons against state-of-the-art dedicated models in digital twin contexts remain limited. This paper makes three contributions. First, we benchmark five well-known TSFMs with frozen backbones on remaining useful life (RUL) prediction using the C-MAPSS dataset, finding that multivariate architectures substantially outperform univariate ones, particularly under varying operating conditions. This raises a deeper question: when cross-channel dependencies can be modeled through pretrained weights, target-task adaptation, and digital twin-derived representations, how much does each contribute, and are they complementary? Second, we propose a topology-informed fusion approach in which topological constraints, derived from the asset structure the digital twin stores among its information models, explicitly shape cross-attention, so that fused representations respect the physical system's local connectivity rather than relying on unconstrained all-to-all interactions. Third, we conduct an ablation study across C-MAPSS subsets of varying operational complexity that isolates the three sources and their interactions. The sources prove complementary rather than redundant, and topology-constrained attention outperforms unconstrained fusion, though by a small margin, enabling a frozen TSFM informed by digital twin representations to remain competitive or in some cases exceed state-of-the-art performance on this regression task.

Predicting the remaining useful life (RUL) is essential for effective predictive maintenance. Spatio-Temporal Graph Neural Networks (ST-GNNs), which can model both temporal and spatial relationships by representing time series data as a sequence of graphs, have shown exceptional performance in RUL prediction. However, current ST-GNNs face several drawbacks. First, they require domain expertise or significant computational power to establish graph structures prior to deploying GNNs. Second, the models are restricted to capture temporal dependencies within a predefined fixed-size lookback window. This restriction ignores the common issue of varying time series lengths, leading the prediction model to miss short-term or long-term dependencies. Finally, conventional models often fail to capture the inherent relationships between samples generated from adjacent time windows, which are crucial for improving both the accuracy and robustness of predictions. To address the aforementioned issues, we introduce a novel framework called Multi-Term Fourier Graph Neural Network with Sample Relationship Learning (MTFGN-SRL). Rather than treating the sample as a sequence of graphs, we consider it as a single complete graph and utilize a Fourier Graph Neural Network (FGN) to capture the spatio-temporal information in the frequency domain. We propose a multi-term learning module that utilizes multiple lookback windows to generate samples with varying terms, which are then fed into the FGN to enhance the extraction of useful information from the data. Finally, we develop a sample relationship learning module by training a heterogeneous GNN to identify inter-sample relationships, resulting in enhanced accuracy and robustness in predictions. Evaluations on the CMAPSS dataset demonstrate MTFGN-SRL's superior performance over state-of-the-art methods in RUL prediction.

Joint remaining useful life (RUL) prediction and capacity estimation require representations of both gradual degradation and recent battery behavior. This paper presents a cross-expert framework using partial-charging measurements without requiring measured historical full-cycle capacity as an input. The RUL Expert captures long-term degradation from nominal 10-min segments sampled across a 30-cycle history, while the Capacity Expert characterizes recent battery behavior from statistical descriptors of nominal 40-min segments over ten consecutive cycles. Their complementary representations are integrated through feature-wise linear modulation for joint RUL and capacity prediction. A key contribution is a three-stage training strategy that progressively controls frozen and trainable components: supervised representation pretraining, independent expert pretraining, and final fusion training with both experts frozen. This staged optimization preserves expert-specific degradation knowledge while improving the balance between the two prediction tasks, with RUL treated as the primary prognostic objective. On two public battery-aging datasets, the reference configuration achieves mean RUL root-mean-square errors of 143.69 and 161.10 cycles and capacity errors of 12.36 and 7.28 mAh, respectively. On Dataset I, cross-expert fusion reduces both mean errors relative to either standalone expert. The proposed framework achieves the lowest reported RUL RMSE among the compared methods on both datasets while maintaining competitive capacity-estimation accuracy.

Significant health risks are associated with the illegal, yet commonly practiced use of industrial-grade Calcium Carbide (CaC2) for ripening climacteric fruits like mango and banana, which leaves behind trace residues of arsenic and phosphorus. To address this, the proposed study explores a novel, non-invasive multispectral framework for distinguishing safely ripened fruits (naturally ripened and ethephon-induced) from calcium carbide-ripened samples, while also estimating their ripening progression (in percentage) and remaining shelf life (in days). The spectral profiles of mango (Mangifera indica) and banana (Musa acuminata) at 18 discrete wavelengths in the visible-near infrared (NIR) range (410 nm - 940 nm) are studied using the AS7265x spectral triad sensor. CaC2-treated samples exhibit sharper spectral intensity drops in the visible region, consistent with accelerated chlorophyll degradation and carotenoid development. To characterize these physiological changes, the feature engineering strategy integrates inter-method spectral variance, intensity ratios at distinct wavelengths, and environmental parameters including temperature and humidity. Dimensionality reduction using Principal Component Analysis (PCA) retains >90% of spectral variance within the first 5-7 components. The resulting feature set is used to train three independent eXtreme Gradient Boosting (XGBoost)-based learning algorithms for ripening method classification, along with quantitative estimation of remaining shelf life and ripening progression. A classification accuracy of 95% along with carbide class recall of 0.67 is observed for mango samples, while the model achieves an accuracy of 81% and carbide class recall of 0.74 for banana. This instrumentation and data-driven approach demonstrates the effectiveness of the proposed non-invasive framework.

Large-scale pretrained time-series models achieve strong results through large-scale pretraining and task-agnostic representation learning, but they rely on abundant, diverse data that industrial and scientific domains often lack. We therefore propose the FSD-RM (Family of Small-Data Representation Models) paradigm as a practical alternative for limited, domain-specific telemetry. Rather than relying on large-scale pretraining, we focus on capacity-controlled representation learning using established encoder architectures (CNN1D, LSTM, GRU, Transformer), selected for their suitability in small-data settings and interpretability. These encoders are trained unsupervised on multivariate telemetry data and integrated into a two-stage pipeline for downstream lifetime prediction. To systematically examine architectural trade-offs under data constraints, we employ \textbf{dimension-aware neural architecture search (NAS)} to jointly optimize model capacity and input dimensionality. Experiments on cryocooler telemetry show that the proposed approach achieves competitive predictive performance while reducing training cost and model complexity. The contribution lies in combining established representation learning techniques within a coherent, NAS-driven framework tailored to small-data regimes, with explicitly defined parameter settings and design choices. The results indicate that effective representation learning can be achieved without large-scale pretraining when appropriate inductive bias and capacity control are applied.

Federated learning (FL) enables aircraft fleet operators to jointly train remaining-useful-life (RUL) models from engine sensor telemetry without sharing raw data. This study examines two complementary challenges: benign heterogeneity, where honest operators observe different operating conditions and fault modes, and adversarial heterogeneity, where compromised operators submit poisoned updates. We conduct a controlled, safety-oriented evaluation using a multi-task one-dimensional convolutional neural network and a structurally non-IID partition of the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) benchmark. We compare four remedies for benign heterogeneity and evaluate five attacks against four aggregation methods, including a physically motivated sensor-value backdoor designed to mask engine degradation. Shared-representation personalization closes approximately 70% of the local-to-centralized root-mean-square-error gap, compared with 21% for proximal regularization and 10% for server-side reweighting. The backdoor achieves a 94.9% attack success rate against standard averaging while leaving clean accuracy statistically unchanged, demonstrating that accuracy alone cannot certify model safety and that attack success must be evaluated explicitly. Krum reduces attack success by an order of magnitude and is the only evaluated aggregator that withstands coordinated attackers, whereas personalization alone provides no protection. Combining personalization with robust aggregation restores robustness (2.8% attack success) with only a small accuracy cost, revealing a trade-off between robust update selection and collaborative representation learning. Results remain consistent across client counts and on a harder six-condition dataset. Code and data partitions are released for reproducibility.

To improve the operational readiness of combat aircraft engines and reduce unplanned maintenance costs, accurately estimating the remaining useful life (RUL) is critical. Traditional maintenance often proves insufficient under dynamic mission profiles. In this study, a deep learning-based predictive maintenance model capable of autonomously extracting features from multivariate sensor data was developed. Using the NASA C-MAPSS FD001 and FD004 datasets, data were converted into sequential blocks via 50- and 30-step sliding windows, respectively. The model's architectural superiority in autonomously extracting temporal degradation features was validated against RF, CNN-LSTM, and BiLSTM baselines. On FD001, it achieved an R-squared (R2) of 0.8901, a 13.28 RMSE, and a 320.34 NASA risk score, demonstrating generalizability on the multi-regime FD004 dataset with a 15.71 RMSE. The proposed maintenance protocol achieved a 0.9973 AUC at the critical 30-cycle threshold, ensuring high reliability. Additionally, a decision-support simulator has been developed to validate this protocol under aggressive combat flight profiles.

Accurate prediction of lithium-ion battery state of health (SOH) is essential for reliable energy storage operation. However, purely data-driven models may generalize poorly across cycling protocols and produce physically implausible behavior during long-term extrapolation. We developed a physics-informed differentiable degradation modeling framework (PiDDM) for battery SOH prediction. PiDDM incorporates empirical Arrhenius degradation kinetics associated with solid electrolyte interphase growth and loss of lithium inventory into the training objective, encouraging physically consistent capacity fade under diverse operating conditions. The framework was evaluated using a public dataset of 55 batteries cycled under six operating protocols. PiDDM achieved the lowest average prediction error among the evaluated models and substantially reduced mean squared error relative to a multilayer perceptron and a baseline physics-informed neural network. For extrapolation, the models were trained on the first 90% of each battery's cycle life and evaluated on the unseen final 10%. PiDDM captured accelerated end-of-life degradation while avoiding the nonphysical capacity regeneration produced by the baseline models. These results show that incorporating degradation physics into neural network training improves predictive accuracy and physical consistency, providing a promising approach for practical battery health monitoring.

Time-to-event modeling provides a systematic framework for estimating time-dependent failure risk, reliability, and remaining useful life (RUL) from longitudinal condition monitoring data. However, applying these models to distributed prognostics remains challenging because sensor trajectories and failure-time records are often stored across organizations or operational sites and cannot be centrally pooled due to privacy or proprietary constraints. Moreover, the classical Cox proportional hazards model relies on a nonseparable partial likelihood involving global risk sets, making direct optimization difficult under standard federated learning protocols. This paper presents a federated longitudinal-survival modeling framework for collaborative system failure prognostics. The proposed framework combines longitudinal sensor representation learning with a client-separable discrete-time hazard objective, enabling multiple clients to collaboratively train a prognostic model without sharing raw sensor measurements or individual failure records. Time-dependent representations extracted from multivariate sensor histories are used to estimate interval-specific failure hazards, reliability curves, and system RUL. Experiments on the four C-MAPSS turbofan engine degradation subsets under simulated decentralized settings demonstrate that the proposed framework consistently improves prognostic performance over isolated local training while maintaining performance comparable to centralized training across heterogeneous operating conditions and failure modes. These results demonstrate the potential of federated longitudinal-survival modeling for collaborative, data-aware condition monitoring and system failure prognostics.

Data-driven remaining useful life (RUL) prediction requires complete degradation trajectories for training, yet such run-to-failure data are scarce and expensive. Practitioners currently lack principled guidance on how many failure examples suffice for a given model and accuracy target. This paper develops a sample complexity framework for RUL prediction comprising seven main results organised around three themes. First, we establish fundamental learning rates: a distribution-free generalization bound shows that the uniform deviation of the mean squared error decreases as $O(B^{2}\sqrt{p/n})$, where $p$ is the model complexity and $n$ the number of trajectories, and a minimax lower bound proves that the $Θ(p/n)$ rate is unimprovable.} \rev{Second, we quantify how domain knowledge accelerates learning: incorporating degradation physics reduces data requirements by up to two orders of magnitude for deep networks, a Bernstein-type analysis achieves the minimax-optimal $O(p/n)$ rate under high signal-to-noise conditions, and closed-form penalties reveal when an incorrectly assumed physics model hurts rather than helps. Third, we characterise the impact of data quality: fleet variability induces an irreducible bias$-$variance tradeoff, while right-censored observations suffer an efficiency loss that depends critically on the degradation class.} Closed-form expressions are provided for exponential, power-law, and stretched-exponential degradation. \rev{Cross-domain validation against published turbofan, battery, and bearing benchmarks confirms the theoretical predictions within a factor of 2$-$3 on average. The results yield practical guidelines for planning data collection, selecting model complexity, and evaluating physics model assumptions in prognostics applications.

Remaining useful life (RUL) prediction and failure-mode classification are central tasks in predictive maintenance. Many data-driven pipelines use fixed-window supervised learning with complete terminal labels; such routes do not naturally encode the temporal recursion linking successive degradation-state predictions when observations are partial or unit identities are unavailable. We formulate prognostics as vector General Value Function (GVF) prediction on an absorbing degradation process, treating RUL and failure-mode probabilities as temporally consistent targets rather than independent window-level labels, and estimate them with a multi-step temporal-difference estimator, TD($n,λ$). Supporting theory identifies the Bellman fixed point of the vector GVFs, characterizes the linear projected-TD limit and its relation to complete-return Monte Carlo regression under realizability, and explains when bootstrapped TD targets are less variable than Monte Carlo returns. On an event-triggered multimode simulation and NASA C-MAPSS label-scarce stitch data, TD improves RUL and failure-mode prediction relative to a supervised same-backbone Monte Carlo control, especially under scarce complete labels. Practically, fragmented, identity-free degradation records can contribute local Bellman transitions instead of being discarded until complete run-to-failure labels are available.

The deployment of reliable lithium-ion battery management systems is crucial for accelerating electrification, yet the joint prognosis of State of Health (SOH) and Remaining Useful Life (RUL) remains severely hindered by task heteroscedasticity. Conventional multi-task learning frameworks fail to balance the bounded, low-variance noise of SOH estimation with the unbounded, nonlinearly expanding uncertainty of long-term RUL predictions. Here, we present the Rotary SOH-Injected Prior Battery Transformer (RoSIP-Batt), a unified co-estimation framework that resolves these optimization conflicts. By formulating joint prediction as a Bayesian multi-task objective, RoSIP-Batt introduces a homoscedastic uncertainty weighting mechanism to dynamically scale task-specific gradients based on learned residual noise levels. The architecture leverages decoupled dual classification tokens and a per-dimension gated fusion mechanism, secured by a gradient-detachment operator to prevent high-variance RUL updates from corrupting the stable SOH representation space. To capture electrochemical degradation patterns without relying on absolute cycle steps, Rotary Position Embedding (RoPE) is incorporated into a shared Transformer backbone to model translation-invariant relative temporal profiles. Crucially, the intermediate SOH estimate is directly injected into the RUL regression head as a physical degradation prior. Evaluations across the NASA, MIT-Stanford, and HUST datasets show that RoSIP-Batt significantly outperforms state-of-the-art baselines, reducing SOH estimation error to 1.994% MAE on NASA and restricting RUL prediction error to 62.85 cycles on Stanford. These findings establish RoSIP-Batt as a highly generalizable, computationally efficient solution suitable for real-time embedded BMS deployment.

The deployment of reliable lithium-ion battery management systems is crucial for accelerating electrification, yet the joint prognosis of State of Health (SOH) and Remaining Useful Life (RUL) remains severely hindered by task heteroscedasticity. Conventional multi-task learning frameworks fail to balance the bounded, low-variance noise of SOH estimation with the unbounded, nonlinearly expanding uncertainty of long-term RUL predictions. Here, we present the Rotary SOH-Injected Prior Battery Transformer (RoSIP-Batt), a unified co-estimation framework that resolves these optimization conflicts. By formulating joint prediction as a Bayesian multi-task objective, RoSIP-Batt introduces a homoscedastic uncertainty weighting mechanism to dynamically scale task-specific gradients based on learned residual noise levels. The architecture leverages decoupled dual classification tokens and a per-dimension gated fusion mechanism, secured by a gradient-detachment operator to prevent high-variance RUL updates from corrupting the stable SOH representation space. To capture electrochemical degradation patterns without relying on absolute cycle steps, Rotary Position Embedding (RoPE) is incorporated into a shared Transformer backbone to model translation-invariant relative temporal profiles. Crucially, the intermediate SOH estimate is directly injected into the RUL regression head as a physical degradation prior. Evaluations across the NASA, MIT-Stanford, and HUST datasets show that RoSIP-Batt significantly outperforms state-of-the-art baselines, reducing SOH estimation error to 1.994% MAE on NASA and restricting RUL prediction error to 62.85 cycles on Stanford. These findings establish RoSIP-Batt as a highly generalizable, computationally efficient solution suitable for real-time embedded BMS deployment.

Predictive maintenance relies on accurate Remaining Useful Life estimation, often formulated using survival analysis over multivariate time-series data. While modern deep survival models achieve strong predictive performance, their black-box nature limits their use in safety-critical settings where actionable insight is required. In this work, we introduce \textit{SurvCF(t)}, the first framework for generating counterfactual explanations for survival models operating on time-series data. \textit{SurvCF(t)} identifies minimal, plausible, and temporally consistent changes to an asset's operational history that increase its predicted life time, framing explanation as a constrained optimization problem combining validity, proximity, sparsity, and plausibility. We evaluate the method on multiple benchmarks, including C-MAPSS, N-CMAPSS, and a real-world case study of the Scania Component_X dataset, demonstrating its ability to produce actionable and interpretable interventions. Our results show that \textit{SurvCF(t)} bridges the gap between survival prediction and prescriptive maintenance, enabling explainable and decision-oriented AI for maintenance strategies.

Supercharging of lithium-ion batteries (LiBs) requires robust health monitoring to ensure durability, safety, and user confidence, particularly for emerging vehicle-to-grid applications with bidirectional energy flows. Yet battery management remains largely disconnected from the material and structural origins of aging, limiting both interpretable health assessment and informed battery design. Here we propose a physics-informed learning framework with virtual sensing that infers hard-to-measure design parameters, including solid-state diffusion coefficient, electrode thickness, ion concentration, and particle size, directly from standard battery management system (BMS) measurements. Across diverse fast-charging strategies and driving profiles, embedding a digital-twin-derived particle-cracking mechanism as a soft constraint reduces trajectory and lifetime prediction errors by 6-8 times relative to state-of-the-art machine learning baselines using only 2% early-life observations. We further show that accurate degradation extrapolation does not require fully resolved governing equations; validated partial mechanisms, jointly refined with limited data, provide sufficient guidance. Virtual sensing transforms standard charging signals into latent design variables without additional sensors, bridging observable battery behavior and underlying aging processes while reducing capacity loss error by up to 39%, end-of-life (EOL) error by 17%, and prediction variability by up to 54%, enabling real-time exploration of new battery configurations. More broadly, the proposed framework establishes a practical feedback loop between deployment and development, demonstrating how real-world operation can continuously inform upstream design decisions across complex multiphysics systems.

Multi-task deep learning models that jointly perform fault classification and remaining useful life (RUL) regression are increasingly used in predictive maintenance, yet reported performance can be strongly affected by how sliding-window sequences are split into training and test sets. We investigate this issue using AMTLNet, an attention-enhanced multi-task architecture, on three public benchmarks: NASA C-MAPSS, NASA IMS, and the UCI Hydraulic System dataset. We show that naive splitting can inflate classification accuracy from a genuine 20-60 percent to 99.9 percent, or reduce it to 0 percent through degenerate class representation. To address this, we introduce a chunk-based, leakage-audited splitting protocol and evaluate all models using five seeds, one-way ANOVA, and Tukey HSD tests. On C-MAPSS, with 19,976 leakage-free training windows, AMTLNet matches a single-task CNN-LSTM baseline in classification, achieving 84.12 +/- 0.96 percent accuracy with Tukey p = 1.0, and reaches an R2 of 0.86 +/- 0.01 while significantly outperforming a naive multi-task baseline. On the smaller Bearing and Hydraulic datasets, multi-task training is unstable, but the failure mode differs: classification degrades for Bearing, whereas regression degrades for Hydraulic. We relate this asymmetry to label provenance and propose a practical framework for deciding when joint training is appropriate under data scarcity. Ablation results show that the multi-head attention branch is the main contributor to regression stability. Removing it reduces R2 from 0.861 to 0.766 and more than doubles classification variance, whereas the convolutional branch contributes little to regression despite using about one-third of the parameters. This study contributes a reusable leakage-audit protocol, seed-transparent evaluation, and evidence that task-specific stability depends more on label provenance than on task type.

Battery health estimation is fundamental for battery management in battery-powered systems, where inaccurate health states may affect control, maintenance, and service life. It becomes even more critical in intelligent connected systems, where estimation errors can propagate across interconnected devices and downstream decisions. In this paper, we propose TIDE, a trustworthy and interpretable battery degradation estimator for reliable battery health estimation. TIDE jointly considers accuracy, trustworthiness, and interpretability, which are all essential for practical deployment and downstream decision making. To realize these objectives, TIDE combines battery-domain knowledge with operational measurements in a three-component backbone. A knowledge-guided degradation prior promotes trustworthy estimation, a monotone residual component provides interpretable aging-consistent refinement, and a contextual learning component captures battery-specific operational effects for improved accuracy. The trained backbone is then distilled into a compact symbolic surrogate to provide model-level interpretability and support deployment. Experiments show that TIDE achieves strong estimation accuracy, improving overall estimation fidelity by an average of 19.7% over representative baselines. Its knowledge-guided prior and monotone residual modelling substantially reduce aging-consistency violations, supporting trustworthy estimation. Meanwhile, the backbone enables component-level interpretation, while symbolic distillation provides a compact model-level representation of the learned estimation logic. These results support the practical use of TIDE for battery health monitoring and decision support in intelligent connected systems.

Long-horizon physics-based simulations of battery degradation provide mechanistic insight but remain computationally expensive, limiting their use for dense exploration of operating conditions over extended cycle life. Here, we propose a hybrid physics-probabilistic learning framework for surrogate modeling of lithium-ion battery degradation trajectories at unseen charging rates. Cycle-resolved degradation data generated with a DFN/P2D electrochemical model in PyBaMM are first transformed into capacity-aligned voltage and derivative features and encoded using a Variational Autoencoder (VAE). The resulting two-dimensional latent space organizes degradation trajectories according to both cycle progression and charging protocol. A sparse multitask Gaussian process (GP) is then trained in this latent space using cycle number and C-rate as input variables, providing continuous interpolation of latent degradation dynamics together with posterior uncertainty estimates. Under protocol-level holdout evaluation, the latent-space GP accurately recovers unseen C-rate trajectories and exhibits uncertainty behavior consistent with the support of the training data. When queried at unseen interior C-rates, the model generates latent trajectories that remain coherently positioned between neighboring simulated protocols. Decoding the GP-predicted latent states through the frozen VAE decoder yields smooth voltage-capacity evolution, while Monte Carlo propagation of the GP latent posterior through an auxiliary latent to State of Health (SOH) predictor provides uncertainty-aware SOH estimates. The proposed BattVAE-GP framework therefore offers a computationally efficient and uncertainty-aware surrogate for long-horizon degradation modeling, providing a structured basis for extending battery health prediction toward richer operating conditions and future simulation-experiment fusion.

Public battery aging datasets are a critical asset for advanced health management, but their practical use is often limited by inconsistent formats, unclear schemas, and metadata scattered across repositories and publications. Current curation remains largely manual and hard to reproduce, while general-purpose data integration tools miss the domain-specific semantics of electrochemical time-series data. We present BatteryLake, a governed data lakehouse that turns raw public battery data into benchmark-ready assets through an agentic, physics-grounded curation framework, with three contributions. First, LLM agents extract metadata and synthesize dataset-specific converters, grounding every output in verbatim evidence and abstaining when none supports a value. Second, a human-in-the-loop mechanism frames verification as selective prediction and gates admitted data through 26 schema, statistical, and physical-plausibility rules. Third, we release an open benchmark of 41 datasets from over 25 institutions, with standardized SOH and RUL tasks, three split protocols, and eight baseline model families. The platform, benchmark, and curation protocol are publicly available at https://tianwen1209.github.io/batterylake/.

Remaining useful life (RUL) estimation is central to predictive maintenance, where an unplanned failure can cost far more than the asset itself. Statistical degradation models miss the strong nonlinearity of real systems, and data-driven models often converge to suboptimal solutions in high-dimensional, non-convex search spaces. We propose a Quantum Annealing enhanced Q-Learning (QAQL) framework that couples the sampling behaviour of quantum annealing with the sequential decision making of Q-learning. Each Q-value update is encoded as a small quadratic unconstrained binary optimization (QUBO) whose ground state is the greedy action; rather than acting as a deterministic optimizer, the annealer returns a distribution over near-optimal actions across many reads, and this stochastic action selection supplies the exploration that curbs premature convergence on nonlinear degradation trajectories. The QUBO is solved on the D-Wave Advantage system using minor embedding, with the annealer woven into the reinforcement-learning loop rather than bolted on after training. We validate QAQL on two public benchmarks: the NASA C-MAPSS turbofan engine datasets and a device-fleet predictive maintenance dataset. Averaged over many independent runs and across six error metrics, QAQL outperforms the classical and quantum baselines considered in this study, with statistically significant improvements. The results indicate that quantum annealing is a usable, not merely theoretical, optimizer inside a reinforcement-learning loop for industrial predictive-maintenance applications.

Remaining Useful Life (RUL) prediction is essential for industrial predictive maintenance, yet many learning-based approaches rely on extensive feature engineering or large labeled datasets to train task-specific sequence models. In this work, we introduce a lightweight learning approach, in which we leverage a frozen pretrained time-series foundation model (TSFM) and combine it with a small regression head for RUL estimation from multivariate sensor streams. More specifically, we use Chronos-2 as a frozen backbone to extract context window features and train a lightweight regression neural network for RUL prediction. Experiments on real-world industrial sensor data from two device types show that Chronos-2 features consistently improve over recurrent, convolutional, Transformer-based, and gradient-boosting baselines under the same preprocessing and evaluation protocol. We further analyze the impact of context length and find that performance improves significantly with longer histories, indicating that TSFM representation offer a practical and data-efficient alternative for RUL estimation in industrial settings.

Data-driven Prognostics and Health Management (PHM) uses time-varying condition-monitoring data to diagnose system states and estimate remaining useful life in engineered assets. These tasks are central to maintenance planning, but industrial PHM data are often fragmented, partially observed, and poorly labeled, which hinders supervised learning. Foundation models offer a route toward reusable predictive systems, yet most time-series foundation models are designed for forecasting and assume long, coherent, regularly sampled sequences. To address this gap, we propose a framework for applying Tabular Foundation Models to industrial time series using in-context learning, and we evaluate them on a variety of PHM tasks. By converting raw unit-level signals into tabular rows, we show that these models perform well across multiple tasks - including prognostics, and diagnostics - and are highly data efficient. We compare them directly with sequence models, transformer baselines, and gradient-boosted trees under a common evaluation protocol. The results indicate that tabular foundation models achieve the best average ranks across prognostic and diagnostic tasks. Our findings further show that PFN-based models are competitive in low-data regimes, that temporal context can be preserved in the tabular representation, and that performance depends on representative context construction under subsampling. These results demonstrate that tabular foundation models provide a practical and general interface for heterogeneous PHM problems.

Accurate Remaining Useful Life prediction is critical for industrial predictive maintenance. However, real-world deployment is challenging due to the irregular nature of sensor observations, characterized by asynchronous sampling, burst missingness, and temporal jitter. Compounding this issue, purely data-driven models often generate physically implausible degradation trajectories that violate the irreversible nature of damage accumulation. To address this, we propose PC-MambaSDE, a unified continuous-time framework for robust RUL prediction under irregular observations. Specifically, we design a Mask-Aware Continuous Mamba Encoder that explicitly leverages observation masks to extract context-rich control signals. Furthermore, we introduce a Physics-Guided Latent SDE with parametrically rectified hybrid drift, superimposing a global physical bias to enforce monotonic degradation even amid severe observation gaps. Additionally, we formulate RUL prediction as a boundary value problem via a Terminal Degradation Penalty, which decouples a Health Index dimension and applies a penalty loss to guide trajectories toward the failure state. Theoretically, we prove that our variational objective is mathematically equivalent to minimizing the KL divergence via Girsanov's theorem, and we guarantee the global asymptotic stability of the learned dynamics through Lyapunov analysis. To enable rigorous evaluation, we develop a Hybrid Irregularity Generation Scheme that simulates realistic industrial imperfections. Extensive experiments on public benchmarks demonstrate that PC-MambaSDE significantly outperforms state-of-the-art methods, particularly under extreme observation scarcity, validating the efficacy of embedding physical priors into continuous-time latent dynamics.

This study presents a novel hybrid prognostic framework for uncertainty-aware Remaining Useful Life (RUL) estimation in turbofan engines using the NASA C-MAPSS dataset. The framework employs a state-aware strategy that bifurcates the engines operational lifespan into "healthy" and "degraded" regimes. An LSTM-based autoencoder, trained strictly on nominal data (RUL > 150 cycles), monitors reconstruction error to act as a robust state classifier. For the healthy regime, a Conditional Weibull Survival Analysis is used for Mean Residual Life estimation. For the degraded regime, a Probabilistic Neural Network with Monte Carlo Dropout captures both aleatoric and epistemic uncertainties. Rather than using rigid binary labels, a calibrated sigmoid function converts the autoencoders output into continuous state probabilities, dynamically weighting the final ensemble prediction. The primary strength of this framework is its generation of physically consistent uncertainty bands, yielding high-confidence predictions near end-of-life while accurately reflecting the inherent variance of early operation, providing a robust tool for risk-informed maintenance.

Engine Health Management (EHM) depends on reliable forecasting of Remaining Useful Life (RUL) and on tracking thermal indicators such as turbine gas temperature (TGT). In practice, real-world fleet data are heterogeneous and non-stationary, and point predictions alone are insufficient for risk-aware maintenance decisions. This paper presents a multi-task scientific machine learning framework for turbine prognostics that jointly predicts turbine gas temperature untrimmed (TGTU), Delta Turbine Gas Temperature (DTGT), and RUL, with quantified uncertainty in the form of prediction intervals whose empirical coverage is evaluated. A shared sequence encoder (convolutional front-end with residual bidirectional LSTM layers and attention pooling) feeds task-specific heads, including mean--variance estimation for probabilistic regression and, optionally, a survival head for threshold-based event modeling. The framework is designed to be tunable via a small set of practitioner-facing parameters (e.g., DTGT thresholding rules and RUL target construction) so that deployment can align with in-house policies and proprietary criteria. The predictive performance of the proposed framework is evaluated using both point and interval metrics, including mean absolute error (MAE), prediction interval coverage probability (PICP), mean prediction interval width (MPIW), and the coverage--width criterion (CWC). Results are reported both in aggregate and stratified by flight phase and maintenance segment to highlight operational-context effects and to support uncertainty-aware monitoring.

Early battery degradation trajectory forecasting (BDTF), which predicts the full-life state-of-health trajectory from early operational data, is critical for battery optimization, manufacturing, and deployment. Battery degradation data exhibit two key characteristics. First, degradation data present a multi-level structure, including regularities shared within aging conditions and trajectory patterns shared across batteries. Second, degradation-related variations in voltage-current profiles are often localized to specific state of charge (SOC) intervals. Existing approaches often fail to explicitly model these characteristics. To bridge this gap, we propose BatteryMFormer, a multi-level Transformer for early BDTF. BatteryMFormer integrates (1) an aging-condition-aware decoder that injects aging-condition priors via aging-condition-informed queries and aging-condition-aware attention, (2) a meta degradation pattern memory that learns and retrieves trajectory prototypes to guide long-horizon forecasting, and (3) a dual-view encoder that jointly captures temporal dynamics and SOC-localized variations from voltage and current time series. Extensive experiments on four battery domains show that BatteryMFormer consistently outperforms state-of-the-art baselines, marking a significant step toward reliable BDTF. Our code is available at https://github.com/Ruifeng-Tan/BatteryMFormer.

Stochastic-process-based degradation modeling is a core approach for estimating the distribution of remaining useful life (RUL); however, the selection of an appropriate stochastic process has not been sufficiently addressed. Existing model selection methods mainly rely on the statistical fit of the observed health indicator (HI) trajectory, but this approach may select a model that is inconsistent with the underlying degradation mechanism when the observation window is short or the signal is highly noisy. To address this issue, this paper proposes Literature-Anchored Stochastic Trajectory Retrieval-Augmented Generation (LAST-RAG). The proposed method uses both the observed HI trajectory and domain-specific context, and hierarchically conditions the candidate degradation model space based on theoretical and mechanical evidence retrieved from a local evidence bank. In addition, Rule-based Confidence Reasoning with Uncertain State (RCRUS) is introduced to prevent candidate models from being prematurely eliminated when hierarchical decisions are uncertain. Simulation-based experiments demonstrate that the proposed method outperforms statistical, prognostic, and uncertainty-aware baselines in both Wiener/gamma family classification and detailed degradation model classification. Ultimately, this study reframes degradation model selection from a purely statistical goodness-of-fit problem into a knowledge-conditioned decision-making problem that integrates observed data with domain knowledge.