2063 research outputs found
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A Bayesian state-space model for tool wear estimation in drilling of Inconel 718
No full textWe study the evolution of tool wear during drilling of plates of Inconel~718 under different cutting speeds. As observable variable we use the spindle motor current, so no additional sensor system is required for monitoring. We propose two Bayesian state-space models with nonlinear dynamics to describe the system, where the latent state (tool wear) is modelled using a modified Gamma process. In our analysis, we also examine the variability from tool to tool --- which is usually neglected --- through a hierarchical model. We apply Bayesian inference to support our conclusions, and we also show a method to deal with missing information due to the difficulty measuring tool wear.- MICIU/AEI/10.13039/501100011033 and ERDF/UE [grant PLEC2024-011247]
- Provincial Council of Bizkaia
- Basque Government grant of excellence groups [IT 1894-26
Understanding Entanglement through the Lens of Quantifiable Algebraic Structures: Application to Bird Navigation
No full textWe propose a unified mathematical meta-framework for long-distance navigation in birds, based on a bundle-theoretic representation of multisensory integration within evolving combinatorial structures. Various information streams—such as magnetic, celestial, olfactory, and landmark cues—are modeled as typed fibers over a time-varying simplicial base, which is reconstructed from behavioral trajectories and neural co-activity.
In this framework, integration is framed as a global consistency problem: coherent system-level repre- sentations occur when there are globally compatible assignments across overlapping local contexts. This is equivalent to finding global sections of an evolving bundle.
The tension between local and global perspectives is formalized in quantum theory through the concept of contextuality, which expresses the impossibility of a single, non-contextual global assignment that is consistent with all local marginals. In Bell-type scenarios, this aligns with operational non-locality and device-independent signatures of entanglement. We demonstrate that the same constraint semantics provide a precise mathematical connection between canonical contextuality models and biological cue integration, treating contextuality as a calculus for diagnosing and localizing incompatibilities in distributed representations.
Our theory introduces two computable topological observables: critical simplices and interface loops. Critical simplices identify discrete remapping pivots where the structural scaffold must be reconfigured to restore consistency, while interface loops detect transient conflict cycles at the boundaries between different information streams. Together, these observables form a diagnostic "compass" that integrates cues onto a common scaffold, localizes incompatible overlaps, and predicts when spatial representations require remapping.
We validate our framework using standard quantum contextuality scenarios, including Bell’s theorem and Klyachko-Can-Binicioglu-Shumovsky model, and successfully recover established contextuality classifications via bundle obstructions and loop signatures. We then apply this framework to an anatomy-aware model of avian navigation, in which entanglement-capable cryptochrome/radical-pair dynamics serve as a microscopic source of non-classical correlations, without assuming that macroscopic entanglement occurs across neural circuits. In this model, microscopic non-classicality influences adaptive functions by leaving persistent, computable contextual footprints within the evolving biological scaffold, providing testable signatures at the level of remapping events and context-dependent cue integration.PID2023-146683OB-100 funded by MICIU/AEI /10.13039/501100011033 and by ERDF, EU
A Copula-based variational autoencoder for uncertainty quantification in inverse problems: application to damage identification in an offshore wind turbine
No full textStructural health monitoring of floating offshore wind Turbines (FOWTs) is critical for ensuring operational safety and efficiency. However, identifying damage in components like mooring systems from limited sensor data poses a challenging inverse problem, often characterized by multiple solutions where various damage states could explain the observed response. To overcome this, we propose a variational autoencoder (VAE) architecture, where the encoder approximates the inverse operator that maps the observed response to the system's condition, while the decoder approximates the forward operator that maps the system's condition and measured excitation to its response.
In the proposed methodology, the observed response corresponds to some representative features derived from short-term rotation motion signals of the FOWT platform. The damage condition is described by the severity level of two damage classes frequently found in the mooring system (anchoring and biofouling).
This work proposes a novel copula-based VAE architecture that decouples the marginal distribution of variables from their dependence structure, thus enabling the representation of complex posterior distributions.
We provide a comprehensive comparison of the copula approximation against standard Gaussian and Gaussian mixture approaches.
Numerical experimentation, conducted on a high-fidelity synthetic dataset, demonstrates that the Gaussian Copula VAE provides a more scalable alternative to Gaussian mixtures in high dimensions.
Indeed, the copula achieves the same performance with significantly fewer parameters than the Gaussian Mixture alternatives, whose parametrization grows prohibitively with the dimensionality of the latent space. These results suggest that copula-based VAEs provide a robust framework for uncertainty-aware damage detection in FOWT mooring systems.Juan de la Cierva Postdoctoral Fellowship under the Grant JDC2023-051132-I funded by MICIU/AEI/10.13039/501100011033 and by the FSE+.
The European Union’s Horizon Europe research and innovation programme under Grant Agreement 101162248 -ORE4Citizens;
The IKUR-HPCAI program (HPCAI7.OceaNNic).
The grant PID2023-146668OA-I00 funded by MICIU / AEI / 10.13039 / 501100011033 and cofunded by the European Union and by grant RYC2022-036312-I funded by MICIU / AEI / 10.13039 / 501100011033 and by ESF+
Evolution-based tool path and motion planning optimization for 5-axis CNC machining of free-form surfaces
No full textManufacturing of free-form geometries using 5-axis Computer Numerically Controlled (CNC) machining brings challenges in path- and motion-planning as one typically wants to minimize the manufacturing time of the object under consideration, while keeping the machining error within fine machining tolerances that ranges in tens of microns. We propose an optimization-based pipeline that, for a given toroidal and/or cylindrical flat-end cutter, simultaneously optimizes its milling paths together with its local positioning represented by the rotation and tilt functions.
The proposed strategy is validated on a variety of benchmark surfaces, with different hyperparameters for the objective function and initial conditions, showing that our results provide high-quality approximations
of free-form geometries using by-construction non-colliding motions of the given tool.PRE2021-099981
RYC-2017-22649
PID2023-146640NB-I00
RYC-2017-2264
Adaptive Multi-task Learning for Probabilistic Load Forecasting
No full textSimultaneous load forecasting across multiple entities
(e.g., regions, buildings) is crucial for the efficient, reliable,
and cost-effective operation of power systems. Accurate
load forecasting is a challenging problem due to the inherent
uncertainties in load demand, dynamic changes in consumption
patterns, and correlations among entities. Multi-task learning has
emerged as a powerful machine learning approach that enables
the simultaneous learning across multiple related problems.
However, its application to load forecasting remains underexplored
and is limited to offline learning methods, which
cannot capture changes in consumption patterns. This paper
presents an adaptive multi-task learning method for probabilistic
load forecasting. The proposed method can dynamically adapt
to changes in consumption patterns and correlations among
entities. In addition, the techniques presented provide reliable
probabilistic predictions for loads of multiple entities and assess
load uncertainties. Specifically, the method is based on vectorvalued
hidden Markov models and uses a recursive process
to update the model parameters and provide predictions with
the most recent parameters. The performance of the proposed
method is evaluated using datasets that contain the load demand
of multiple entities and exhibit diverse and dynamic consumption
patterns. The experimental results show that the presented techniques
outperform existing methods both in terms of forecasting
performance and uncertainty assessment.PID2022-137063NB-I00
Verónica Álvarez holds a postdoctoral grant from the Basque Government
An optimal fractional Hardy inequality on the discrete half-line
No full textIn the context of Hardy inequalities for the fractional Laplacian on the discrete half-line , we provide an optimal Hardy-weight for exponents . As a consequence, we provide an estimate of the sharp constant in the fractional Hardy inequality with the classical Hardy-weight on . It turns out that for the Hardy-weight is pointwise larger than the optimal Hardy-weight obtained by Keller--Pinchover--Pogorzelski near infinity.
As an application of our main result, we obtain unique continuation results at infinity for the solutions of some fractional Schr\"odinger equation.CNS2023-143893
PID2023-146646N
Scattering and Pairing by Exchange Interactions
Full text linkQuantum interactions exchanging different types of particles play a pivotal rôle in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspective. Here, we consider a system made of two fermions and one boson, in order to study the effect of such an off-diagonal interaction term, having in mind the physics of cuprate superconductors. Additionally, our model also includes a generalized Hubbard interaction (i.e., a general local repulsion term for the fermions). Regarding pairing, exponentially localized dressed bound fermion pairs are shown to exist and their effective dispersion relation is studied in detail. Scattering properties of the system are derived for two channels: the unbound and bound pair channels. We give particular attention to the regime of very large on-site (Hubbard) repulsions, because this situation is relevant for cuprate superconductors.This work is supported by the COST Action CA18232 financed by the European Cooperation in Science and Technology (COST) and also by the Basque Government through the grant IT1615-22 and BERC 2022-2025 program and by the Ministry of Science and Innovation: PID2020-112948GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe"
Optimizing Variational Physics-Informed Neural Networks Using Least Squares
No full textVariational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a least squares solver for the weights of the last layer of the neural network, we improve the convergence of the loss during training in most practical scenarios. This work analyzes the computational cost of the resulting hybrid least-squares/gradient-descent optimizer and explains how to implement it efficiently. In particular, we show that a traditional implementation based on backward-mode automatic differentiation leads to a prohibitively expensive algorithm. To remedy this, we propose using either forward-mode automatic differentiation or an ultraweak-type scheme that avoids the differentiation of trial functions in the discrete weak formulation. The proposed alternatives are up to one hundred times faster than the traditional one, recovering a computational cost-per-iteration similar to that of a conventional gradient-descent-based optimizer alone. To support our analysis, we derive computational estimates and conduct numerical experiments in one- and two-dimensional problems
Data augmentation for damaged scenarios in floating offshore wind turbines: an approach based on diffusion architecture, hierarchical variational approximation and healthy data distribution
No full textDeveloping digital twin and condition monitoring models for Floating Offshore Wind Turbines (FOWTs) mooring systems requires massive data across various health, operational, and metocean conditions. The scarcity of real damage-associated data may represent a significant challenge. Deep generative models (DGMs) have recently been introduced as powerful tools for oversampling scarce data. However, most oversampling methods focus on minority intra-class information. The inter-class dynamics between minority and majority classes are often ignored, increasing the risk of overfitting, especially in scenarios with high imbalance ratios. This study proposes a novel hierarchical variational autoencoder (HVAE) utilizing the diffusion probabilistic architecture, healthy (majority) data distribution, and the relation between healthy and damage-associated data in mooring systems of FOWTs to learn the damaged state distribution. We first evaluate HVAE’s ability to augment minority data based on majority distribution, using the MNIST benchmark image dataset for validation. This experiment compares the performance of HVAE with conventional and recent oversampling techniques. The second use case is the OC4-DeepCWind FOWT benchmark. The fine-tuned HVAE can generate damage-associated platform records for various sea states. Experimental results on MNIST indicate that HVAE achieves significant improvements over alternative oversampling techniques in downstream classification tasks, particularly in case of extreme imbalance. In the FOWT use case, the records generated for unseen sea states can incorporate the diversity and complexity of the majority ones, hence decreasing overfitting for the majority of sea states in downstream binary classification, highlighting the efficacy and generalization of HVAE
Computational Modelling of Thixotropic Multiphase Fluids
Full text linkMultiphase systems are ubiquitous in engineering, biology, and materials science, where understanding their complex interactions and rheological behavior is crucial for advancing applications ranging from emulsion stability to cellular phase separation. This study presents a numerical methodology for modeling thixotropic multiphase fluids, emphasizing the transient behavior of viscosity and the intricate interactions between phases. The model incorporates phase-dependent viscosities, interfacial tension effects, and the dynamics of phase separation, coalescence, and break-up, making it suitable for simulating systems with complex flow regimes. A key feature of the methodology is its ability to capture thixotropic behavior, where viscosity evolves over time due to microstructural changes induced by shear history. This approach enables the simulation of aging and recovery processes in materials such as gels, emulsions, and biological tissues. The model is rigorously validated against benchmark cases, demonstrating its accuracy in predicting multiphase systems under static and dynamic conditions. Subsequently, the methodology is applied to investigate systems with varying levels of microstructural evolution, revealing the impact of thixotropic dynamics on overall system behavior. The results provide new insights into the time-dependent rheology of multiphase fluids and highlight the versatility of the model for applications in industrial and biological systems involving complex fluid interactions