We are interested in the application of a statistical change detection approach to the problem of structural health monitoring of mechanical structures excited by the ambient vibrations. More particularly, the proposed subject relates to the study of the algorithms of localization of damages and their bond with the finite elements models and methods. More precisely, our statistical approach is based on the construction of a residual vector built from data collected on the structure in operation and of a model of reference, a collection of parameters and functions calculated beforehand on the healthy structure. The confrontation of both gives an alarm which reacts when the new data significantly differ - from the statistical point of view - from the reference model.
The vector residue takes into account the parameters to monitor through a Jacobian collecting the sensitivities of the residue with respect to the interesting parameters. In the case of a simple monitoring, whose goal is only to know if damage has occurred, the number of parameters is relatively low, and the Jacobean can be of full rank. Then, provided that the residue is well calculated, one obtains a problem not degenerated. When a great number of parameters is concerned, which is the case for the problems of localization on structures with the finite elements, the number of finite elements (typically several thousands) exceeds by far the number of statistical parameters (a hundred) which supervises the residue. The number of unknown factors - for example the variation of the masses and stiffness of each finite element - becomes too high. An immediate consequence is the impossibility of distinguishing from a statistical point of view certain finite elements: those will react in the same way to the test whatever their state is healthy or damaged. If two elements have this property of nonseparability, then a reaction of the residue will imply that at least one of both is damaged. We will call macro class, a set of elements having this property. For the same macro class, it is useless to practice the monitoring on more than one representing of the class. It is thus interesting to know in advance the distribution of these classes in the structure. He is an also important to study the modification of the class repetition with respect to a variation in the sensor positioning: various sets of sensors do not have the same properties of separability and thus do not provide the same classes.
Two approaches are possible:
The candidate for the postdoctoral position must have knowledge in two fields: on the one hand statistical methods of identification, in particular those based on algorithms of the stochastic realization type for discrete linear systems; and in addition, the reduction of model problems for the structures with the finite elements, as well as the associated methods of sub structuring. An unquestionable taste for the experimentation and algorithm implementation is strongly wished.