Health monitoring for strongly non‐linear systems using the Ensemble Kalman filter

Many structural engineering problems of practical interest involve pronounced non-linear dynamics the governing laws of which are not always clearly understood. Standard identification and damage detection techniques have difficulties in these situations which feature significant modelling errors and strongly non-Gaussian signals. This paper presents a combination of the ensemble Kalman filter and non-parametric modelling techniques to tackle structural health monitoring for non-linear systems in a manner that can readily accommodate the presence of non-Gaussian noise. Both location and time of occurrence of damage are accurately detected in spite of measurement and modelling noise. A comparison between ensemble and extended Kalman filters is also presented, highlighting the benefits of the present approach. Copyright © 2005 John Wiley & Sons, Ltd

Compressive sensing adaptation for polynomial chaos expansions

Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorithms, resulting in a reduced polynomial chaos approximation with optimal sparsity. The developed adaptation algorithm consists of a two-step optimization procedure that computes the optimal coefficients and the input projection matrix of a low dimensional chaos expansion with respect to an optimally rotated basis. We demonstrate the attractive features of our algorithm through several numerical examples including the application on Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE scramjet engine.Comment: Submitted to Journal of Computational Physic

Equation-Free Dynamic Renormalization: Self-Similarity in Multidimensional Particle System Dynamics

We present an equation-free dynamic renormalization approach to the computational study of coarse-grained, self-similar dynamic behavior in multidimensional particle systems. The approach is aimed at problems for which evolution equations for coarse-scale observables (e.g. particle density) are not explicitly available. Our illustrative example involves Brownian particles in a 2D Couette flow; marginal and conditional Inverse Cumulative Distribution Functions (ICDFs) constitute the macroscopic observables of the evolving particle distributions.Comment: 7 pages, 5 figure

Vida Verde. Barcelona

International audienceWe demonstrate, on a scramjet combustion problem, a constrained probabilistic learning approach that augments physics-based datasets with realizations that adhere to underlying constraints and scatter. The constraints are captured and delineated through diffusion maps, while the scatter is captured and sampled through a projected stochastic differential equation. The objective function and constraints of the optimization problem are then efficiently framed as non-parametric conditional expectations. Different spatial resolutions of a large-eddy simulation filter are used to explore the robustness of the model to the training dataset and to gain insight into the significance of spatial resolution on optimal design

Inverse Problems in a Bayesian Setting

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.Comment: arXiv admin note: substantial text overlap with arXiv:1312.504

Anatomical projections of the dorsomedial hypothalamus to the periaqueductal grey and their role in thermoregulation: a cautionary note

The DMH is known to regulate brown adipose tissue (BAT) thermogenesis via projections to sympathetic premotor neurons in the raphe pallidus, but there is evidence that the periaqueductal gray (PAG) is also an important relay in the descending pathways regulating thermogenesis. The anatomical projections from the DMH to the PAG subdivisions and their function are largely elusive, and may differ per anterior-posterior level from bregma. We here aimed to investigate the anatomical projections from the DMH to the PAG along the entire anterior-posterior axis of the PAG, and to study the role of these projections in thermogenesis in Wistar rats. Anterograde channel rhodopsin viral tracing showed that the DMH projects especially to the dorsal and lateral PAG. Retrograde rabies viral tracing confirmed this, but also indicated that the PAG receives a diffuse input from the DMH and adjacent hypothalamic subregions. We aimed to study the role of the identified DMH to PAG projections in thermogenesis in conscious rats by specifically activating them using a combination of canine adenovirus-2 (CAV2Cre) and Cre-dependent designer receptor exclusively activated by designer drugs (DREADD) technology. Chemogenetic activation of DMH to PAG projections increased BAT temperature and core body temperature, but we cannot exclude the possibility that at least some thermogenic effects were mediated by adjacent hypothalamic subregions due to difficulties in specifically targeting the DMH and distinct subdivisions of the PAG because of diffuse virus expression. To conclude, our study shows the complexity of the anatomical and functional connection between the hypothalamus and the PAG, and some technical challenges in studying their connection