Virtual Sensing

Spatial flow measurements support underwater navigation, but distributed sensing is constrained by robot size and sensor layout. We use a causal observer to estimate current lateral velocities from a finite history of measurements collected by a single sensing unit, supplying the inputs of a fixed navigation controller. In two-dimensional wake simulations with access to body-frame ambient velocity, this virtual sensing interface reduces simultaneous flow sampling from three points to the robot center. Trained only in a circular-cylinder wake at Re = 100, the flow-history observer achieves 84.4% and 80.6% success at held-out Re = 205 and 240 without retraining. These rates are 7.4 and 4.6 percentage points below direct spatial sensing and more than 30 points above a matched current-only observer. Past flow remains beneficial when past goal and yaw information is available. Across obstacle geometries, performance remains close to direct sensing in square-prism wakes but declines in triangular-prism wakes. Component replacement identifies the lateral velocity difference as control-relevant, while controlled perturbations reveal sensitivity to error persistence. The results demonstrate the closed-loop utility of single-point flow histories under the assumed observation model.

Virtual sensing, the estimation of hard-to-measure quantities from available sensor measurements, is a critical enabler for control and monitoring in cyber-physical systems. However, when sensors fail, learning-based predictors can produce physically implausible estimates that propagate to system-level failures. We argue that real-world deployment demands robustness and introduce MuViS-C, the first multi-domain benchmark of robustness against common sensor failures in learning-based virtual sensing. Building on an existing nominal-performance benchmark and established corruption taxonomies, it covers ten sensor failure modes, from subtle drifts to catastrophic signal dropouts, at multiple severities. These are paired with complementary robustness measures capturing average error under corruption, relative degradation, and worst-case fragility. Across nine datasets from six domains, we benchmark six architectures spanning gradient-boosted trees and the major inductive biases for sequence modeling: convolution, recurrence, attention, and MLP-mixing. On the attention-based architecture, we further probe three robustification strategies. We find that (i) every model degrades substantially under corruption, becoming worse than a naïve predictor on at least one corruption setting, (ii) gradient-boosted tree ensembles achieve strong robustness, and (iii) dedicated robustification closes the gap between the attention-based architecture and the most robust models, though each strategy hurts nominal performance. The benchmark's multi-domain design proves essential, as model rankings shift across datasets, and no single domain captures the full robustness picture. MuViS-C is open-source and extensible to new datasets, failure modes, measures, and models.

Virtual sensing enables digital twins and safety-critical systems to reconstruct and forecast spatial-temporal physics in real time. However, conventional computational and data-driven methods often face challenges in generalization, latency, and energy efficiency for edge deployment. Neural operators offer a promising alternative but remain reliant on power-intensive hardware. Spiking neurons and neuromorphic computing can improve efficiency, yet surrogate-gradient training and multi-step spiking introduce convergence and latency challenges. We propose the Sparse-Activation-ReLU (SAR) layer, a single-step alternative that promotes activation sparsity without surrogate-gradient training while remaining compatible with event-based computing. Within a trunk-based NOMAD architecture, SAR achieves over a fivefold improvement in the combined Latency-Error-Energy (LEE) metric compared with Variable Spiking Neuron (VSN) and Leaky Integrate-and-Fire (LIF) implementations. We further analyze spiking entropy and feature usage and introduce synthetic knowledge distillation, reducing the LEE score by more than twofold. Finally, we improve VSN through a ReLU-based spiking loss and graph-neighbor thresholding. On the Heat Exchanger dataset, these approaches reduce L2 error by more than twofold and nearly sevenfold, respectively, while reducing spiking and spatial aggregation. Overall, the work presented is a step towards energy-efficient virtual sensing by providing an alternative framework that can be positioned towards neuromorphic or other edge device integration that can be a gold standard to compare latency, energy, and error performance for future efficient designs that are sparsity or brain-inspired spiking based.

Accurate modeling and forecasting of power transformer thermal behavior are critical for reliability, asset lifetime, and optimized power system operation. Numerical approaches such as finite element methods (FEM) and computational fluid dynamics (CFD) offer high fidelity but are computationally expensive, require complex mesh generation, and are often impractical for real-time or large-scale applications, particularly when transformer geometries are unknown. Lumped-parameter thermal models are more practical but depend on transformer-specific thermal constants and may fail to capture dynamic responses under varying operating and environmental conditions. Purely data-driven machine learning methods, including artificial neural networks, convolutional neural networks, and long short-term memory (LSTM) networks, have shown success in forecasting transformer temperatures but typically require large volumes of high-quality training data and may produce physically inconsistent or uninterpretable results. This paper develops a physics-aware Neural Ordinary Differential Equation (Neural ODE) framework for forecasting transformer thermal behavior from real-world time-series data. Neural ODEs model system dynamics in continuous time, providing smooth trajectory prediction and a natural representation of continuously evolving thermal dynamics. A key contribution is the integration of simplified heat-transfer equations directly into the Neural ODE formulation. The model is evaluated across datasets from fifteen transformers in different regions of Norway with varying designs and cooling mechanisms. The results demonstrate that the developed Neural ODE framework provides a standardized, physics-aware, and robust forecasting approach for heterogeneous transformer units.

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.

Modern IoT and sensor networks generate vast amounts of data, posing significant challenges for storage, transmission, and real-time processing. Traditional approaches, such as compressive sensing and machine learning-based compression, often suffer from computational inefficiencies and irreversible data loss. This paper introduces Information Density as a quantitative metric to support sensor deployment and enable AI-driven virtual sensing. We propose a framework that leverages spatial, temporal and inter-modal correlations among sensor signals to perform sensing tasks even in the absence of physical sensors. Two complementary measures: (i) Phase in Eigen Space and (ii) Mutual Information, are developed to quantify and assess information density, enabling the selection of optimal sensor configurations across both intra-modality and cross-modality scenarios. Validated using real-world data from Madrid's smart city infrastructure, this framework demonstrates the feasibility of replacing physical sensors with virtual ones under bounded error conditions (e.g., achieving $<3.21\%$ mean error with a single sensor). The results highlight the potential for scalable and energy-efficient sensing systems in smart environments.

Monitoring high-dimensional engineering structures in extreme environments is limited by non-stationary excitation, nonlinear structural kinematics, and stochastic forcing. Traditional model-based and black-box data-driven methods often struggle to resolve these dynamics in real time, particularly under sensor failure or partial observability. This paper introduces a rank-optimized digital twin framework based on Koopman operator theory, Hankel-matrix embeddings, and dynamic mode decomposition. By lifting operational data into a linear invariant subspace, the method enables autonomous, input-blind reconstruction of structural states without requiring a priori mass or stiffness matrices. The framework is validated on an NREL 5MW spar-buoy floating offshore wind turbine, representing a challenging coupled aero-hydro-servo-elastic system. Results show that the rank-optimized Koopman-Hankel manifold separates structural resonances from deterministic 3P rotor harmonics under colored noise, where standard subspace identification can be unreliable. A rolling-horizon virtual sensing strategy achieves high-fidelity reconstruction at critical structural hotspots, with coefficient of determination greater than 0.95 at 1 Hz data assimilation and accuracy exceeding 0.99 at higher sampling rates. By estimating a physical Lyapunov time of approximately 1.0 s, the study defines the predictability horizon associated with the system information barrier. The proposed framework provides a computationally efficient and resilient digital twin approach for real-time identification and virtual sensing of complex structural dynamics.

Digital twins provide a powerful paradigm for diagnostic and prognostic tasks in the monitoring and control of engineered systems; however, their deployment for complex structures remains challenged by model-form uncertainty, arising from unknown nonlinear dynamics, and by sparse sensing. These limitations hinder reliable online state estimation using either purely physics-based or purely data-driven approaches. This work introduces the Physics-Guided Graph Neural ODE (PiGGO) framework, a physics-informed, graph-based Bayesian state estimation approach in which a learned graph neural ordinary differential equation (GNODE) serves as the continuous-time state-transition model within an extended Kalman filter. The graph representation explicitly defines the system state-space, while physics-guided inductive biases encode known structural relationships and constrain the learning of nonlinear dynamics. By integrating graph-native learned dynamics with recursive Bayesian filtering, the proposed PiGGO framework enables online virtual sensing and uncertainty-aware state estimation for nonlinear systems with unknown model form, while maintaining generalisation across topologically similar structures. Numerical case studies demonstrate improved robustness to model uncertainty and measurement noise, outperforming both open-loop graph neural models and conventional filtering approaches in online prediction tasks.

Predicting full-field physics through the real-time virtual sensing of engineering systems can enhance limited physical sensors but often requires sparse-to-dense reconstruction, complex multiphysics, and highly irregular geometries as well as strict latency and energy constraints for edge-deployability. Neural operators have been presented as a potential candidate for such applications but few architectures exist that explicitly address power consumption. Spiking neuron integration can provide a potential solution when integrated on neuromorphic hardware but the current existing neuron models result in severe performance degradation towards regression-based virtual sensing. To address the performance concerns and edge-constraints, we present the Variable Spiking Graph Neural Operator (VS-GNO) which integrates a sophisticated spectral-spatial convolutional analysis and a previously developed Variable Spiking Neuron (VSN) and energy-error balance loss function. With a non-spiking $L_2$ error baseline of $0.4\%$, VS-GNO can provide a reconstruction error of $0.71\%$ with $15\%$ average spiking in its spectral-only form and $1.04\%$ with $24.5\%$ spiking in its entire form. These results position VS-GNO as a promising step towards energy-efficient, edge-deployable neural operators for real-time sparse-to-dense virtual sensing in complex, highly irregular engineering environments.