Approximate observability and back and forth observer of a PDE model of crystallisation process

In this paper, we are interested in the estimation of Particle Size Distributions (PSDs) during a batch crystallization process in which particles of two different shapes coexist and evolve simultaneously. The PSDs are estimated thanks to a measurement of an apparent Chord Length Distribution (CLD), a measure that we model for crystals of spheroidal shape. Our main result is to prove the approximate observability of the infinite-dimensional system in any positive time. Under this observability condition, we are able to apply a Back and Forth Nudging (BFN) algorithm to reconstruct the PSD

Avoiding observability singularities in output feedback bilinear systems

Control-affine output systems generically present observability singularities, i.e. inputs that make the system unobservable. This proves to be a difficulty in the context of output feedback stabilization, where this issue is usually discarded by uniform observability assumptions for state feedback stabilizable systems. Focusing on state feedback stabilizable bilinear control systems with linear output, we use a transversality approach to provide perturbations of the stabilizing state feedback law, in order to make our system observable in any time even in the presence of singular inputs

A stochastic 3-scale method to predict the thermo-elastic behaviors of polycrystalline structures

The purpose of this work is to upscale material uncertainties in the context of thermo-elastic response of polycrystalline structures. The probabilistic behavior of micro-resonators made of polycrystalline materials is evaluated using a stochastic multi-scale approach defined using the following methodology. 1. Stochastic volume elements (SVEs) [1] are defined from Voronoi tessellations using experimental measurements of the grain size, orientation, and surface roughness [2]; 2. Mesoscopic apparent thermo-elastic properties such as elasticity tensor, thermal conductivity tensor, and thermal dilatation tensor are extracted using a coupled homogenization theory [3, 4] applied on the SVE realizations; 3. A stochastic model of the homogenized properties extracted from Voronoi tessellations using a moving window technique is then constructed in order to be able to generate spatially correlated meso-scale random fields; 4. These meso-scale random fields are then used as input for stochastic finite element simulations. As a result, the probabilistic distribution of micro-resonator properties can be extracted. The applications are two-fold: 1. A stochastic thermo-elastic homogenization, see Fig. 1(a), is coupled to thermoelastic 3D models of the micro-resonator in order to extract the probabilistic distribution of the quality factor of micro-resonators [5]; 2. A stochastic second-order mechanical homogenization, see Fig. 1(b), is coupled to a plate model of the micro-resonator in order to extract the effect of the uncertainties related to the surface roughness of the polycrystalline structures [2]. References [1] Ostoja-Starzewski, M., Wang, X. Stochastic finite elements as a bridge between random material microstructure and global response. Comput. Meth. in Appl. Mech. and Eng. (1999) 168: 35-49. [2] Lucas, V., Golinval, J.-C., Voicu, R., Danila, M., Gravila, R., Muller, R., Dinescu, A., Noels, L., Wu, L. Propagation of material and surface profile uncertainties on MEMS micro-resonators using a stochastic second-order computational multi-scale approach. Int. J. for Num. Meth. in Eng. (2017). [3] Temizer, I., Wriggers, P. Homogenization in finite thermoelasticity.J. of the Mech. and Phys. of Sol. (2011) 59, 344-372. [4] Nguyen, V. D., Wu, L., Noels, L. Unified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method. Computat. Mech. (2017) 59, 483-505. [5] Wu, L., Lucas, V., Nguyen, V. D., Golinval, J.-C., Paquay, S., Noels, L. A Stochastic Multi-Scale Approach for the Modeling of Thermo-Elastic Damping in Micro-Resonators. Comput. Meth. in Appl. Mech. and Eng. (2016) 310, 802-839.3SMVIB: The research has been funded by the Walloon Region under the agreement no 1117477 (CT-INT 2011-11-14) in the context of the ERA-NET MNT framework. Experimental measurements provided by IMT Bucharest (Voicu Rodica, Baracu Angela, Muller Raluca

Propagation of uncertainties in the modelling of MEMS resonators (using a 3-scale probabilistic approach)

In order to ensure the accuracy of MEMS vibrometers, the first resonance frequency should be predicted at the design phase. However, this prediction is subjected to randomness: there is a scatter in the reached value resulting from the uncertainties involved in the manufacturing process. The purpose of this work is to take into account these uncertainties of the microstructure. The objective is a non-deterministic model that can be used since the design stage. The material is the source of uncertainties: the beam resonator is made of a polycrystalline material in which each grain has a random orientation. Solving the problem with a full direct numerical simulation combined to a Monte-Carlo method allows the probability density function of the resonance frequency to be computed. However this methodology is computationally expensive due to the number of degrees of freedom required to study one sample, motivating the development of a computationally efficient method. Towards this end a 3-scales stochastic model for predicting the resonance frequency of a micro-beam made of a polycrystalline linear anisotropic material is described. At the lower scale, we model the micro-structure with micro-volume elements. Due to the small-scale involved, the representativity of these micro-volume elements is not achieved and thus Statistical Volume Elements (SVE) are considered. These SVEs are generated under the form of a Voronoï tessellation, each grain being assigned a random orientation. Computational homogenization is applied over the SVEs, along with a Monte-Carlo procedure, to obtain a stochastic characterization of the elasticity tensor at the second scale of interest, the meso-scale. The spatial correlation between SVEs is also estimated. A generator based on spectral methods is implemented. Afterwards, using a stochastic finite element method, these meso-scale uncertainties are propagated by taking account of the spatial correlation up to the higher scale to predict the probabilistic behavior of the MEMS resonator.3SMVIB: The research has been funded by the Walloon Region under the agreement no 1117477 (CT-INT 2011-11-14) in the context of the ERA-NET MNT framework

Dynamic Output Feedback Stabilization of Non-uniformly Observable Dissipative Systems

Output feedback stabilization of control systems is a crucial issue in engineering. Most of these systems are not uniformly observable, which proves to be a difficulty to move from state feedback stabilization to dynamic output feedback stabilization. In this paper, we present a methodology to overcome this challenge in the case of dissipative systems by requiring only target detectability. These systems appear in many physical systems and we provide various examples and applications of the result

A stochastic computational multiscale approach; Application to MEMS resonators

peer reviewedThe aim of this work is to develop a stochastic multiscale model for polycrystalline materials, which accounts for the uncertainties in the micro-structure. At the finest scale, we model the micro-structure using a random Voronoi tessellation, each grain being assigned a random orientation. Then, we apply a computational homogenization procedure on statistical volume elements to obtain a stochastic characterization of the elasticity tensor at the meso-scale. A random field of the meso-scale elasticity tensor can then be generated based on the information obtained from the SVE simulations. Finally, using a stochastic finite element method, these meso-scale uncertainties are propagated to the coarser scale. As an illustration we study the resonance frequencies of MEMS micro-beams made of poly-silicon materials, and we show that the stochastic multiscale approach predicts results in agreement with a Monte Carlo analysis applied directly on the fine finite-element model, i.e. with an explicit discretization of the grains.3SMVIB: The research has been funded by the Walloon Region under the agreement no 1117477 (CT-INT 2011-11-14) in the context of the ERA-NET MNT framework

Cardiomyocyte Protection by Hibernating Brown Bear Serum: Toward the Identification of New Protective Molecules Against Myocardial Infarction

Ischemic heart disease remains one of the leading causes of death worldwide. Despite intensive research on the treatment of acute myocardial infarction, no effective therapy has shown clinical success. Therefore, novel therapeutic strategies are required to protect the heart from reperfusion injury. Interestingly, despite physical inactivity during hibernation, brown bears (Ursus arctos) cope with cardiovascular physiological conditions that would be detrimental to humans. We hypothesized that bear serum might contain circulating factors that could provide protection against cell injury. In this study, we sought to determine whether addition of bear serum might improve cardiomyocyte survival following hypoxia-reoxygenation. Isolated mouse cardiomyocytes underwent 45 min of hypoxia followed by reoxygenation. At the onset of reoxygenation, cells received fetal bovine serum (FBS; positive control), summer (SBS) or winter bear serum (WBS), or adult serums of other species, as indicated. After 2 h of reoxygenation, propidium iodide staining was used to evaluate cell viability by flow cytometry. Whereas, 0.5% SBS tended to decrease reperfusion injury, 0.5% WBS significantly reduced cell death, averaging 74.04 +/- 7.06% vs. 79.20 +/- 6.53% in the FBS group. This cardioprotective effect was lost at 0.1%, became toxic above 5%, and was specific to the bear. Our results showed that bear serum exerts a therapeutic effect with an efficacy threshold, an optimal dose, and a toxic effect on cardiomyocyte viability after hypoxia-reoxygenation. Therefore, the bear serum may be a potential source for identifying new therapeutic molecules to fight against myocardial reperfusion injury and cell death in general