Jean-Claude Golinval

Sensor validation using principal component analysis

For a reliable on-line vibration monitoring of structures, it is necessary to have accurate sensor information. However, sensors may sometimes be faulty or may even become unavailable due to failure or maintenance activities. The problem of sensor validation is therefore a critical part of structural health monitoring. The objective of the present study is to present a procedure based on principal component analysis which is able to perform detection, isolation and reconstruction of a faulty sensor. Its efficiency is assessed using an experimental application.

Principal Component Analysis of a Piezosensor Array for Damage Localization

This paper focuses on applying statistical process control techniques, based on principal component analysis, to vibration-based damage diagnosis. It is well known that localized structural damages with relative small amplitude do not affect much the global modal response of the structure, at least at low frequencies. Nevertheless, it can be expected that the local dynamic behavior of a damaged structural subcomponent is significantly affected. Assuming that each structural subcomponent is monitored, local structural damage, with relative small amplitude, will only affect a particular sensor without affecting significantly the response of the others. By applying a principal component analysis on the sensor time responses, it is possible to see that any change of one particular sensor will affect the subspace spanned by the complete sensor response set. The subspace corresponding to the damaged structure can then be compared with the subspace of an initial state in order to diagnose possible damage. The principal component analysis may also be performed for every potential subset of damaged sensors in order to identify the involved sensor, and, therefore, the damaged structural component. The spatial information given by the distributed sensors (e.g. piezoelectric laminates) can be used to forecast structural damages on a critical area but damage localization is also possible with classical sensors (e.g. accelerometers). The damage may be located as the errors attain the maximum at the sensors instrumented in the damaged substructures.

Identification of a continuous structure with a geometrical non-linearity. Part I: Conditioned reverse path method

Particular effort has been spent in the field of identification of multi-degree-of-freedom non-linear systems. The newly developed methods permit the structural analyst to consider increasingly complex systems. The aim of this paper and a companion paper is to study, by means of two methods, a continuous non-linear system consisting of an experimental cantilever beam with a geometrical non-linearity. In this paper (Part I), the ability of the conditioned reverse path method, which is a frequency domain technique, to identify the behaviour of this structure is assessed. The companion paper (Part II) is devoted to the application of proper orthogonal decomposition, which is an updating technique, to the test example.

Structural damage diagnosis by Kalman model based on stochastic subspace identification

This paper presents an application of statistical process control techniques for damage diagnosis using vibration measurements. A Kalman model is constructed by performing a stochastic subspace identification to fit the measured response histories of the undamaged (reference) structure. It will not be able to reproduce the newly measured responses when damage occurs. The residual error of the prediction by the identified model with respect to the actual measurement of signals is defined as a damage-sensitive feature. The outlier statistics provides a quantitative indicator of damage. The advantage of the method is that model extraction is performed by using only the reference data and that no further modal identification is needed. On-line health monitoring of structures is therefore easily realized. When the structure consists of the assembly of several sub-structures, for which the dynamic interaction is weak, the damage may be located as the errors attain the maximum at the sensors instrumented in the damaged sub-structures.

Bayesian Model Screening for the Identification of Nonlinear Mechanical Structures

The development of techniques for identification and updating of nonlinear mechanical structures has received increasing attention in recent years. In practical situations, there is not necessarily a priori knowledge about the nonlinearity. This suggests the need for strategies that allow inference of useful information from the data. The present study proposes an algorithm based on a Bayesian inference approach for giving insight into the form of the nonlinearity. A family of parametric models is defined to represent the nonlinear response of a system and the selection algorithm estimates the likelihood that each member of the family is appropriate. The (unknown) probability density function of the family of models is explored using a simple variant of the Markov Chain Monte Carlo sampling technique. This technique offers the advantage that the nature of the underlying statistical distribution need not be assumed a priori. Enough samples are drawn to guarantee that the empirical distribution approximates the true but unknown distribution to the desired level of accuracy. It provides an indication of which models are the most appropriate to represent the nonlinearity and their respective goodness-of-fit to the data. The methodology is illustrated using two examples, one of which comes from experimental data.

Identification of a continuous structure with a geometrical non-linearity. Part II: Proper orthogonal decomposition

Particular effort has been spent in the field of identification of multi-degree-of-freedom non-linear systems. The newly developed methods permit the structural analyst to consider increasingly complex systems. The aim of this paper and a companion paper is to study, by means of two methods, a continuous non-linear system consisting of an experimental cantilever beam with a geometrical non-linearity. In the companion paper (Part I) [1] the ability of the conditioned reverse path method, which is a frequency domain technique, to identify the behaviour of this structure is assessed. This paper (Part II) is devoted to the application of proper orthogonal decomposition, which is an updating technique, to the test example.

Modal Analysis of a Nonlinear Periodic Structure with Cyclic Symmetry

This paper carries out modal analysis of a nonlinear periodic structure with cyclic symme- try. The nonlinear normal mode (NNM) theory is brie°y described, and a computational algorithm for the NNM computation is presented. The results obtained on a simpli¯ed model of a bladed assembly show that this system possesses a very complicated struc- ture of NNMs, including similar and nonsimilar NNMs, nonlocalized and localized NNMs, bifurcating and internally resonant NNMs. Modal interactions that occur without neces- sarily having commensurate natural frequencies in the underlying linear system are also discussed.

Feature extraction using auto-associative neural networks

Modal analysis is now mature and well accepted in the design of mechanical structures. It determines the vibration mode shapes and the corresponding natural frequencies. However, the validity of modal analysis is limited to structures showing a linear behaviour. In non-linear structural dynamics, it is well known that mode shapes are no longer useful for the characterization of the dynamic response. The purpose of the present paper is to define new features which efficiently capture the dynamics of a non-linear structure. The proposed methodology takes advantage of auto-associative neural networks to compute one-dimensional curves which allow for non-linear dependences between the coordinates. Synthetic data sampled from a non-linear normal mode motion are used to illustrate the method and to develop intuition about its implementation.

Nonlinear Modal Analysis of a Full-Scale Aircraft

Nonlinear normal modes, which are defined as a nonlinear extension of the concept of linear normal modes, are a rigorous tool for nonlinear modal analysis. The objective of this paper is to demonstrate that the computation of nonlinear normal modes and of their oscillation frequencies can now be achieved for complex, real-world aerospace structures. The application considered in this study is the airframe of the Morane–Saulnier Paris aircraft. Ground vibration tests of this aircraft exhibited softening nonlinearities in the connection between the external fuel tanks and the wing tips. The nonlinear normal modes of this aircraft are computed from a reduced-order nonlinear finite element model using a numerical algorithm combining shooting and pseudo-arclength continuation. Several nonlinear normal modes, involving, e.g., wing bending, wing torsion, and tail bending, are presented, which highlights that the aircraft can exhibit very interesting nonlinear phenomena. Specifically, it is shown that modes with ...

A Micro–Macroapproach to Predict Stiction due to Surface Contact in Microelectromechanical Systems

Stiction, which results from contact between surfaces, is a major failure mode in microelectromechanical systems (MEMS). Indeed, microscopic structures tend to adhere to each other when their surfaces come into contact and when the restoring forces are unable to overcome the interfacial forces. Since incidental contacts cannot be completely excluded and since contacts between moving parts can be part of the normal operation of some types of MEMS, stiction prediction is an important consideration when designing micro- and nanodevices. In this paper, a micro-macro multiscale approach is developed in order to predict possible stiction. At the lower scale, the unloading adhesive contact-distance curves of two interacting rough surfaces are established based on a previously presented model [L. Wu , J. Appl. Phys. 106, 113502, 2009]. In this model, dry conditions are assumed, and only the van der Waals forces as adhesion source are accounted for. The resulting unloading adhesive contact-distance curves are dependent on the material, surface properties such as elastic modulus and surface energy, and rough surface topography parameters (the standard deviation of asperity heights and the asperity density). At the higher scale, a finite element analysis is considered to determine the residual cantilever beam configuration due to the adhesive forces once contact happens. Toward this end, the adhesive contact-distance curve computed previously is integrated on the surface of the finite elements as a contact law. The effects of the design parameters can then be studied for the given material and surface properties.