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See detailA Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
Hoang Truong, Vinh ULg; Wu, Ling ULg; Paquay, Stéphane et al

in Micro and Nanomechanics (in press)

Adhesion is an important phenomenon in the context of MEMS for which the surface forces become dominant in comparison with the body forces. Because the magnitudes of the adhesive forces strongly depend on ... [more ▼]

Adhesion is an important phenomenon in the context of MEMS for which the surface forces become dominant in comparison with the body forces. Because the magnitudes of the adhesive forces strongly depend on the surface interaction distances, which in turn evolve with the roughness of the contacting surfaces, the adhesive forces cannot be determined in a deterministic way. To quantify the uncertainties on the structural stiction behavior of a MEMS, this work proposes a “stochastic multi-scale methodology”. The key ingredient of the method is the evaluation of the random meso-scale apparent contact forces, which homogenize the effect of the nano-scale roughness and are integrated into a numerical model of the studied structure as a random contact law. To obtain the probabilistic behavior at the structural MEMS scale, a direct method needs to evaluate explicitly the meso-scale apparent contact forces in a concurrent way with the stochastic multi-scale approach. To reduce the computational cost, a stochastic model is constructed to generate the random meso-scale apparent contact forces. To this end, the apparent contact forces are parameterized by a vector of parameters before applying a polynomial chaos expansion in order to construct a mathematical model representing the probability of the random parameters vector. The problem of micro-beam stiction is then studied in a probabilistic way. [less ▲]

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See detailMulti-scale stochastic study of the grain orientation and roughness effects on polycrystalline thin structures
Lucas, Vincent ULg; Wu, Ling ULg; Golinval, Jean-Claude ULg et al

Conference (2016, June 09)

When studying micro-electro-mechanical systems (MEMS) made of poly-crystalline materials, as the size of the device is only one or two orders of magnitude higher than the size of the the grains, the ... [more ▼]

When studying micro-electro-mechanical systems (MEMS) made of poly-crystalline materials, as the size of the device is only one or two orders of magnitude higher than the size of the the grains, the structural properties exhibit a scatter at the macro-scale due to the existing randomness in the grain size, grain orientation, surface roughness... In order to predict the probabilistic behavior at the structural scale, the authors have recently developed a stochastic 3-scale approach [1]. In this method, stochastic volume elements (SVEs) [2] are defined by considering random grain orientations in a tessellation. For each SVE realization, a meso-scopic apparent material tensor can be obtained using the computational homogenization theory. The extracted meso-scopic apparent material tensors can then be used to defined a spatially correlated meso-scale random field, which is in turn used as input for stochastic finite element simulations. In this work we intend to study the effect of different material-related uncertainty sources on the structural behavior of vibrating micro-devices manufactured using low pressure chemical vapor deposition. First, the effect of preferred grain orientation on vibrating micro-structures is assessed. To this end, SVEs are generated so that their grain orientation distributions follow XRD measurements. Second, the effect of the roughness of the vibrating micro-structures is studied. Toward this end, SVEs, whose rough surface statistical properties follow AFM measurements, are generated. A second-order computational homogenization [3] applied on the different SVE realizations allows defining a meso-scale random field of the in-plane and out-of-plane meso-scale shell properties. Stochastic shell finite elements can then be applied to predict the MEMS probabilistic behavior. [1] V. Lucas, et al., Comp. Meth. in Appl. Mech. and Eng., 294, 141-167, 2015 [2] M. Ostoja-Starzewski, X.Wang, Comp. Meth. in Appl. Mech. and Eng., 168, 35–49, 1999 [3] E.W.C. Coenen, V. Kouznetsova, M.G.D. Geers. Int. J. for Numer. Meth. in Eng., 83, 1180–1205, 2010. [less ▲]

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See detailA Stochastic Multi-scale Model For Predicting MEMS Stiction Failure
Hoang Truong, Vinh ULg; Paquay, Stéphane; Golinval, Jean-Claude ULg et al

in Proceedings of the SEM XIII International Congress and Exposition on Experimental and Applied Mechanics. (SEMXIII 2016) (2016, June 06)

Adhesion is an important phenomenon in the context of MEMS for which the surface forces become dominant in comparison with the body forces. Because the magnitudes of the adhesive forces strongly depend on ... [more ▼]

Adhesion is an important phenomenon in the context of MEMS for which the surface forces become dominant in comparison with the body forces. Because the magnitudes of the adhesive forces strongly depend on the surface interaction distances, which in turn evolve with the roughness of the contacting surfaces, the adhesive forces cannot be determined in a deterministic way. To quantify the uncertainties on the structural stiction behavior of a MEMS, this work proposes a “stochastic multi-scale methodology”. The key ingredient of the method is the evaluation of the random meso-scale apparent contact forces, which homogenize the effect of the nano-scale roughness and are integrated into a numerical model of the studied structure as a random contact law. To obtain the probabilistic behavior at the structural MEMS scale, a direct method needs to evaluate explicitly the meso-scale apparent contact forces in a concurrent way with the stochastic multi-scale approach. To reduce the computational cost, a stochastic model is constructed to generate the random meso-scale apparent contact forces. To this end, the apparent contact forces are parameterized by a vector of parameters before applying a polynomial chaos expansion in order to construct a mathematical model representing the probability of the random parameters vector. The problem of miro-beam stiction is then studied in a probabilistic way. [less ▲]

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See detailInfluence of the inter‐stage coupling flexibility on the dynamics of multi‐stage rotors
Nyssen, Florence ULg; Golinval, Jean-Claude ULg

in Proceedings of the ASME Turbo Expo 2016 (2016, June)

In this work, a characterization of the inter-stage coupling in a one-piece multi-stage bladed structure is performed. More particularly, the effect of the inter-stage coupling flexibility on the mode ... [more ▼]

In this work, a characterization of the inter-stage coupling in a one-piece multi-stage bladed structure is performed. More particularly, the effect of the inter-stage coupling flexibility on the mode-shapes is evaluated. To this purpose, the MAC matrix between the mono-stage and multi-stage modes is computed for different drum Young’s modulus of the inter-stage coupling. In parallel, the strain energy located in the blades and in the connecting structure is computed for different levels of inter-stage coupling. This enables to establish a criterion to determine when a multi-stage finite element analysis is necessary instead of only computing the different mono-stage models separately. This criterion is based on the localization of the energy in the structure. Numerical analyses are performed on a two-stages academic bladed structure. [less ▲]

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See detailProbabilistic prediction of the quality factor of micro-resonator using a stochastic thermo-mechanical multi-scale approach
Wu, Ling ULg; Lucas, Vincent ULg; Nguyen, Van Dung ULg et al

Scientific conference (2016, May 23)

As the size of the device is only one or two orders of magnitude higher than the size of the grains, the structural properties, such as the thermo-elastic quality factor (Q), of micro-electro-mechanical ... [more ▼]

As the size of the device is only one or two orders of magnitude higher than the size of the grains, the structural properties, such as the thermo-elastic quality factor (Q), of micro-electro-mechanical systems (MEMS) made of poly- crystalline materials exhibit a scatter, due to the existing randomness in the grain size, grain orientation, surface roughness. In order to predict the probabilistic behavior of micro-resonators, the authors extend herein a previously developed stochastic 3-scale approach to the case of thermoelastic damping. In this method, stochastic volume elements (SVEs) are defined by considering random grain orientations in a tessellation. For each SVE realization, the mesoscopic apparent elasticity tensor, thermal conductivity tensor, and thermal dilatation tensor can be obtained using thermo-mechanical computational homogenization theory. The extracted mesoscopic apparent properties tensors can then be used to define a spatially correlated mesoscale random field, which is in turn used as input for stochastic finite element simulations. As a result, the probabilistic distribution of the quality factor of micro-resonator can be extracted by considering Monte-Carlo simulations of coarse-meshed micro-resonators, accounting implicitly for the random microstructure of the poly-silicon material. [less ▲]

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See detailA Study Of Dry Stiction Phenomenon In MEMS Using A Computational Stochastic Multi-scale Methodology
Hoang Truong, Vinh ULg; Wu, Ling ULg; Paquay, Stéphane et al

in EuroSimE 2016 in Montpellier (2016, April 19)

This work studies the uncertainties of the adhesive contact problems for reduced size structures, e.g. the stiction failure of microelectromechanical systems (MEMS). In MEMS, because of the large surface ... [more ▼]

This work studies the uncertainties of the adhesive contact problems for reduced size structures, e.g. the stiction failure of microelectromechanical systems (MEMS). In MEMS, because of the large surface to volume ratio, the surfaces forces, such as van der Waals forces and capillary forces, are dominant in comparison with the body forces. As these force magnitudes strongly depend on the contact distance, when the two contacting surfaces are rough, the contact distances vary, and the physical contact areas are limited at the highest asperities of the contacting surfaces. Therefore, the adhesive contact forces between two rough surfaces can suffer from a scatter, and the involved structural behaviors can be indeterministic. To numerically predict the probability behaviors of structures involving adhesion in dry environments, in this paper, a computational stochastic model-based multi-scale method developed by the authors is applied. The effects of van der Waals is studied and compared with experimental data as well as with the effects of capillary forces. [less ▲]

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See detailDynamic calibration of piezoelectric transducers for ballistic high-pressure measurement
Elkarous, Lamine ULg; Robbe, Cyril; Pirlot, Marc et al

in International Journal of Metrology and Quality Engineering (2016)

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See detailMultivariate ARMA Based Modal Identification of a Time-varying Beam
Bertha, Mathieu ULg; Golinval, Jean-Claude ULg

in Proceedings of the International Modal Analysis Conference (IMAC) XXXIV (2016)

The present paper addresses the problem of modal identification of time-varying systems. The identification is based on a multivariate autoregressive moving-average model in which the time variability of ... [more ▼]

The present paper addresses the problem of modal identification of time-varying systems. The identification is based on a multivariate autoregressive moving-average model in which the time variability of the system is caught using a basis functions approach. In this approach, the time-varying regressive coefficients in the model are expended in the chosen basis functions and only the projection coefficients have to be identified. In that way, the initial time-varying problem then becomes a time-invariant one that can be solved. Because a multivariate model is used, in addition to the time-varying poles, the time-varying mode shapes may be identified too. The method is first presented and then applied on an experimental demonstration structure. The experimental structure consists of a supported beam on which a mass is travelling. The mass is chosen sufficiently large to have a significant influence on the dynamics of the primary system. This kind of problem is a classical example commonly used by many authors to test time-varying identification methods. [less ▲]

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See detailA probabilistic model for predicting the uncertainties of the humid stiction phenomenon on hard materials
Hoang Truong, Vinh ULg; Wu, Ling ULg; Paquay, Stéphane et al

in Journal of Computational & Applied Mathematics (2015), 289

Stiction is a major failure in microelectromechanical system (MEMS) devices in which two contacting surfaces can remain stuck together because of the adhesive forces. Due to the difference between the ... [more ▼]

Stiction is a major failure in microelectromechanical system (MEMS) devices in which two contacting surfaces can remain stuck together because of the adhesive forces. Due to the difference between the surfaces roughness and the adhesive force range, the real contact areas are usually smaller than the apparent one, resulting in a scatter in the adhesive forces. Consequently, the stiction is an uncertain phenomenon. In this work, we develop a probabilistic model to predict the uncertainties of stiction due to the capillary forces acting on stiff materials. This model contains two levels: at the deterministic level, the model can predict the pull-out adhesive contact forces for a given surface topology; at the probabilistic level, the model generates independent identically distributed surfaces on which the deterministic solution can be applied to evaluate the uncertainties related to the stiction phenomenon. [less ▲]

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See detailA stochastic computational multiscale approach; Application to MEMS resonators
Lucas, Vincent ULg; Golinval, Jean-Claude ULg; Paquay, Stéphane et al

in Computer Methods in Applied Mechanics & Engineering (2015), 294

The 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 ... [more ▼]

The 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. [less ▲]

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See detailA probabilistic multi-scale model for polycrystalline MEMS resonators
Lucas, Vincent ULg; Wu, Ling ULg; Paquay, Stéphane et al

Conference (2015, July 09)

The size of micro-electro-mechanical systems (MEMS) is only one or two orders of magnitude higher than the size of their micro-structure, i.e. their grain size. As a result, the structural properties ... [more ▼]

The size of micro-electro-mechanical systems (MEMS) is only one or two orders of magnitude higher than the size of their micro-structure, i.e. their grain size. As a result, the structural properties exhibit a scatter. As an example we study the beam resonator illustrated in Fig. 1(a), made of poly-silicon 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 to be computed as illustrated in Fig. 1(b). However this methodology is computationally expensive due to the number of degrees of freedom required to study one sample, motivating the development of a non-deterministic 3-scale approach [3]. In a multiscale approach, at each macro-point of the macro-structure, the resolution of a microscale boundary value problem relates the macro-stress tensor to the macro-strain tensor. At the micro-level, the macro-point is viewed as the center of a Representative Volume Element (RVE). The resolution of the micro-scale boundary problem can be performed using finite-element simulations, as in the computational homogenization framework, e.g. [2]. However, to be representative, the micro-volume-element should have a size much bigger than the microstructure size. In the context of the MEMS resonator, this representativity is lost and Statistical Volume Elements (SVE) are considered. These SVEs are generated under the form of a Voronoi tessellation with a random orientation for each silicon grain. Hence, a Monte-Carlo procedure combined with a homogenization technique allows a distribution of the material tensor at the meso-scale to be estimated. The correlation between the meso-scale material tensors of two SVEs separated by a given distance can also be evaluated. A generator at the meso-scale based on the spectral method [4] is implemented. The generator [3] accounts for a lower bound [1] of the meso-scale material tensor in order to ensure the existence of the second-order moment of the Frobenius norm of the generated material tensor inverse [5]. Using the random meso-scale field obtained with the meso-scale generator, which accounts for the spatial correlation, a Monte-Carlo method can be used at the macro-scale to predict the probabilistic behavior of the MEMS resonator. [less ▲]

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See detailPropagation of uncertainties in the modelling of MEMS resonators (using a 3-scale probabilistic approach)
Lucas, Vincent ULg; Wu, Ling ULg; Golinval, Jean-Claude ULg et al

Conference (2015, May 26)

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 ... [more ▼]

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. [less ▲]

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See detailA stochastic multiscale analysis for MEMS stiction failure
Hoang Truong, Vinh ULg; Wu, Ling ULg; Golinval, Jean-Claude ULg et al

Conference (2015, May 26)

Stiction is a major failure in microelectromechanical system (MEMS) devices in which two contacting surfaces can remain stuck together because of the adhesive forces, such as van der Waals forces and ... [more ▼]

Stiction is a major failure in microelectromechanical system (MEMS) devices in which two contacting surfaces can remain stuck together because of the adhesive forces, such as van der Waals forces and capillary forces. Stiction is a multiscale problem which is characterized by three different lengths: the MEMS device characteristic length, the roughness of the contacting surfaces, and the distance range of the adhesive forces. Because MEMS surfaces roughness and adhesive force distances are of comparable scales, the randomness in the contacting surfaces can result in important uncertainties on the interacting forces, and in turn lead to a scatter in the MEMS structural behavior. The purpose of this work is to quantify the uncertainties on the macro stiction behavior of a MEMS structure due to the randomness in its contacting surfaces. A full analysis, such as the combination of a Monte-Carlo simulation to generate random surfaces combined with finite element (FE) analyses to model the stiction behavior, is expensive in terms of the computational cost due to the difference in the scales between the macro characteristic length and the distance range of the adhesive forces. Thus, in this work, we develop a stochastic multiscale analysis. At the micro scale, the uncertainties in the interacting forces between two rough surfaces are investigated. The power spectral density function of the surface is characterized from experimental topology measurements, and interacting surfaces are then generated as Gaussian random surfaces. For each generated random surface, the interacting adhesive forces are calculated by using a modified Dejarguin-Muller-Toporov (DMT) model. The resulting adhesive contact forces can be integrated using the finite element method at the structural scale by associating to each discretized contacting point a sampled surface. We then use the Monte-Carlo method to quantify the uncertainties in the stiction behavior of the MEMS device. [less ▲]

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See detailPropagation of uncertainties using probabilistic multi-scale models
Lucas, Vincent ULg; Wu, Ling ULg; Paquay, Stéphane et al

Conference (2015, February 25)

When applying a multiscale approach, the material behavior at the macro-scale can be obtained from an homogenization scheme. To this end, at each integration-point of the macro-structure, the macrostress ... [more ▼]

When applying a multiscale approach, the material behavior at the macro-scale can be obtained from an homogenization scheme. To this end, at each integration-point of the macro-structure, the macrostress tensor is related to the macro-strain tensor through the resolution of a micro-scale boundary value problem. At the micro-level, the macro-point is viewed as the center of a Representative Volume Element (RVE). However, to be representative, the micro-volume-element should have a size much bigger than the micro-structure size. When considering structures of reduced sizes, such as micro-electro-mechanical systems (MEMS), as the size of the devices is only one or two orders of magnitude higher than the size of their microstructure, i.e. their grain size, the structural properties exhibit a scatter at the macro-scale. The representativity of the micro-scale volume element is lost and Statistical Volume Elements (SVE) should be considered in order to account for the micro-structural uncertainties. These uncertainties should then be propagated to the macro-scale in order to predict the device properties in a probabilistic way. In this work we propose a non-deterministic multi-scale approach [1] for poly-silicon MEMS resonators. A set of SVEs is first generated under the form of Voronoi tessellations with a random orientation assigned for each silicon grain of each SVE. The resolution of each micro-scale boundary problem is performed by recourse to the computational homogenization framework, e.g. [2], leading to meso-scale material properties under the form of a linear material tensor for each SVE. Applying a Monte-Carlo procedure allows a distribution of this material tensor to be determined at the meso-scale. The correlation between the meso-scale material tensors of two SVEs separated by a given distance can also be evaluated. A generator of the meso-scale material tensor is then implemented using the spectral method [3]. The generator [1] accounts for a lower bound [4] of the meso-scale material tensor in order to ensure the existence of the second-order moment of the Frobenius norm of the tensor inverse [5]. A macro-scale finite element model of the beam resonator can now be achieved using regular finite-element, i.e. not conforming with the grains, and the material tensor at each Gauss point is obtained using the meso-scale generator, which accounts for the spatial correlation. A Monte-Carlo method is then used at the macro-scale to predict the probabilistic behavior of the MEMS resonator. As an example the beam resonator illustrated in Fig. 1(a) is made of poly-silicon, and 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 to be computed as illustrated in Fig. 1(b). However this methodology is computationally expensive due to the number of degrees of freedom required to study one sample. The proposed non-deterministic multi-scale strategy allows reducing this computational cost as the Monte-Carlo processes are applied on much smaller finite-element models. The method can also be applied in the context of fracture of thin poly-silicon film [6]. In this case, a set of meso-scopic cohesive laws can be obtained at the meso-scale from the resolution of different SVEs. The meso-scopic cohesive laws are obtained for each RVE from the finite element resolution of the Voronoi tessellations using the method proposed in [7]. The resulting statistical values for the critical energy release rate and for the critical strength can then be used for macro-scale simulations. [less ▲]

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See detailIdentification of Mistuning and Model Updating of an Academic Blisk Based on Geometry and Vibration Measurements
Nyssen, Florence ULg; Golinval, Jean-Claude ULg

in Mechanical Systems & Signal Processing (2015)

In this work, an experimental modal analysis is performed on an academic bladed disk using a base excitation to identify the mistuning of each blade. Optical measurement is used to obtain the exact ... [more ▼]

In this work, an experimental modal analysis is performed on an academic bladed disk using a base excitation to identify the mistuning of each blade. Optical measurement is used to obtain the exact geometry of the structure and to be able to associate geometrical mistuning to each blade. Differences are observed between the experimentally identified mistuning and the geometrical mistuning. Since the bladed disk is a one-piece structure, there are no welded connections between the blades and the disk and the material properties can be assumed to be uniform. It can be shown that these differences come from nonuniform clamping conditions, and that this mistuning is of the same order of magnitude than the variations in the geometry of the structure. It follows that the precise characterisation of mistuning for industrial structures is in practice illusory because of the numerous factors introducing mistuning, such as the clamping conditions, aerodynamic damping, wear in service, etc. [less ▲]

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See detailOn the Use of Principal Component Analysis for Parameter Identification and Damage Detection in Structures
Golinval, Jean-Claude ULg

Conference (2014, November 20)

Modal analysis is used extensively for understanding the dynamic behaviour of structures as well as for structural health monitoring or damage detection based on output-only measurements. In this ... [more ▼]

Modal analysis is used extensively for understanding the dynamic behaviour of structures as well as for structural health monitoring or damage detection based on output-only measurements. In this presentation, a different approach based on principal component analysis is considered. Principal component analysis (PCA), also called proper orthogonal decomposition (POD), is a multi-variate statistical method that aims at obtaining a compact representation of the data. In the present paper, PCA (POD) is used for three purposes, namely damage detection, structural health monitoring and identification of nonlinear parameters. The key idea of PCA is to reduce a large number of measured data to a much smaller number of uncorrelated variables while retaining as much as possible of the variation in the original data. To this purpose, an orthogonal transformation to the basis of the eigenvectors of the sample covariance matrix is performed, and the data are projected onto the subspace spanned by the eigenvectors corresponding to the largest eigenvalues. This transformation has the property to decorrelate the signal components and to maximize variance. The first problem to which PCA is applied here is the damage detection problem. When applied to vibration measurements, it can be shown that the basis of eigenvectors (called the proper orthogonal modes) span the same subspace as the mode-shape vectors of the monitored structure. Thus the damage detection problem may be solved using the concept of subspace angle between a reference subspace spanned by the eigenvectors of the initial (undamaged) structure and the subspace spanned by the eigenvectors of the current (possibly damaged) structure. The second problem concerns structural health monitoring of civil engineering structures when environmental effects (e.g. the influence of the variation of the ambient temperature) have to be removed from the structural changes. In this case, PCA may be applied on identified modal features (e.g. the natural frequencies) to separate the changes due to environmental variations from the changes due to damage sources. This procedure is illustrated on the example of a real bridge located in Luxembourg. The third problem is related to the estimation of nonlinear parameters using model updating techniques. In this case, the most interesting property of PCA is that it minimizes the average squared distance between the original signal and its reduced linear representation. When applied to nonlinear problems, PCA gives the optimal approximating linear manifold in the configuration space represented by the data. The linear nature of the method is appealing because the theory of linear operators is still available. However, it should be borne in mind that it also exhibits its major limitation when the data lie on a nonlinear manifold. [less ▲]

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See detailPrediction of meso-scale mechanical properties of poly-silicon materials
Lucas, Vincent ULg; Wu, Ling ULg; Arnst, Maarten ULg et al

Conference (2014, August 27)

The miniature sizes of micro–electro–mechanical systems (MEMS) as well as the nature of their manufacturing processes, such as etching, material layer deposition, or embossing, are responsible for the ... [more ▼]

The miniature sizes of micro–electro–mechanical systems (MEMS) as well as the nature of their manufacturing processes, such as etching, material layer deposition, or embossing, are responsible for the existence of a scatter in the final dimensions, material properties ... of manufactured micro–sensors. This scatter is potentially threatening the behavior and reliability of samples from a batch fabrication process, motivating the development of non-deterministic computational approaches to predict the MEMS properties. In this work we extract the meso-scale properties of the poly-silicon material under the form of a probabilistic distribution. To this end, Statistical Volume Elements (SVE) of the micro-structure are generated under the form of a Voronoï tessellation with a random orientation for each silicon grain. Hence, a Monte-Carlo procedure combined with a homogenization technique allows a distribution of the material tensor at the meso-scale to be estimated. As the finite element method is used to discretize the SVE and to solve the micro-scale boundary value problem, the homogenization technique used to extract the material tensor relies on the computational homogenization theory. In a future work, we will investigate, in the context of MEMS vibrometers, the propagation to the macro–scale of the meso-scale distribution of the homogenized elasticity tensor, with the final aim of predicting the uncertainty on their resonance frequencies. [less ▲]

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See detailModeling of Uncertainties in Bladed Disks Using a Nonparametric Approach
Nyssen, Florence ULg; Arnst, Maarten ULg; Golinval, Jean-Claude ULg

in Proceedings of the ASME IDETC/CIE 2014 (2014, August)

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See detailExperimental modal analysis of a beam travelled by a moving mass using Hilbert Vibration Decomposition
Bertha, Mathieu ULg; Golinval, Jean-Claude ULg

Scientific conference (2014, July)

In this paper the problem of modal identification of time-varying system is investigated. To do so, a technique based on the sifting process of the Hilbert Vibration Decomposition (HVD) method is ... [more ▼]

In this paper the problem of modal identification of time-varying system is investigated. To do so, a technique based on the sifting process of the Hilbert Vibration Decomposition (HVD) method is presented. The key idea is to estimate the instantaneous frequency of the dominant mode, to extract its corresponding component by demodulation of the recorded signals and then to iterate with the subsequent dominant mode. In the case of multiple recorded signals, a source separation method is used as a preprocessing step to facilitate the identification of the instantaneous frequency for the following demodulation step. To illustrate the method, an experimental set-up consisting in a beam travelled by a non negligible mass is considered. The whole structure is randomly excited during the travel of the mass and some responses on the beam are recorded. [less ▲]

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